3446:
351:
3544:. This usually means isolating the system from its environment as interactions with the external world cause the system to decohere. However, other sources of decoherence also exist. Examples include the quantum gates, and the lattice vibrations and background thermonuclear spin of the physical system used to implement the qubits. Decoherence is irreversible, as it is effectively non-unitary, and is usually something that should be highly controlled, if not avoided. Decoherence times for candidate systems in particular, the transverse relaxation time
2731:
4115:; that is, all problems that can be efficiently solved by a deterministic classical computer can also be efficiently solved by a quantum computer, and all problems that can be efficiently solved by a quantum computer can also be solved by a deterministic classical computer with polynomial space resources. It is further suspected that BQP is a strict superset of P, meaning there are problems that are efficiently solvable by quantum computers that are not efficiently solvable by deterministic classical computers. For instance,
33:
4039:
3437:. However, the immense size and complexity of the structural space of all possible drug-like molecules pose significant obstacles, which could be overcome in the future by quantum computers. Quantum computers are naturally good for solving complex quantum many-body problems and thus may be instrumental in applications involving quantum chemistry. Therefore, one can expect that quantum-enhanced generative models including quantum GANs may eventually be developed into ultimate generative chemistry algorithms.
12234:
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2704:
resulting state encodes the function's output values for all input values in the superposition, allowing for the computation of multiple outputs simultaneously. This property is key to the speedup of many quantum algorithms. However, "parallelism" in this sense is insufficient to speed up a computation, because the measurement at the end of the computation gives only one value. To be useful, a quantum algorithm must also incorporate some other conceptual ingredient.
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example in chemistry and materials science. However, the article also concludes that a large range of the potential applications it considered, such as machine learning, "will not achieve quantum advantage with current quantum algorithms in the foreseeable future", and it identified I/O constraints that make speedup unlikely for "big data problems, unstructured linear systems, and database search based on Grover's algorithm".
13551:
626:
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2940:, adiabatic quantum computation, and topological quantum computationâhave been shown to be equivalent to the quantum Turing machine; given a perfect implementation of one such quantum computer, it can simulate all the others with no more than polynomial overhead. This equivalence need not hold for practical quantum computers, since the overhead of simulation may be too large to be practical.
2281:
3680:, generally considered the world's fastest computer. This claim has been subsequently challenged: IBM has stated that Summit can perform samples much faster than claimed, and researchers have since developed better algorithms for the sampling problem used to claim quantum supremacy, giving substantial reductions to the gap between Sycamore and classical supercomputers and even beating it.
199:
2038:
2900:, which are algorithms that run on a realistic model of quantum computation, can be computed equally efficiently with neuromorphic quantum computing. Both, traditional quantum computing and neuromorphic quantum computing are physics-based unconventional computing approaches to computations and donât follow the
2832:. One common such set includes all single-qubit gates as well as the CNOT gate from above. This means any quantum computation can be performed by executing a sequence of single-qubit gates together with CNOT gates. Though this gate set is infinite, it can be replaced with a finite gate set by appealing to the
4123:
are known to be in BQP and are suspected to be outside of P. On the relationship of BQP to NP, little is known beyond the fact that some NP problems that are believed not to be in P are also in BQP (integer factorization and the discrete logarithm problem are both in NP, for example). It is suspected
3596:
to suppress errors and decoherence. This allows the total calculation time to be longer than the decoherence time if the error correction scheme can correct errors faster than decoherence introduces them. An often-cited figure for the required error rate in each gate for fault-tolerant computation is
3230:
by brute force requires time equal to roughly 2 invocations of the underlying cryptographic algorithm, compared with roughly 2 in the classical case, meaning that symmetric key lengths are effectively halved: AES-256 would have the same security against an attack using Grover's algorithm that AES-128
3136:
in the agricultural fertilizer industry (even though naturally occurring organisms also produce ammonia). Quantum simulations might be used to understand this process and increase the energy efficiency of production. It is expected that an early use of quantum computing will be modeling that improves
2034:
The mathematics of single qubit gates can be extended to operate on multi-qubit quantum memories in two important ways. One way is simply to select a qubit and apply that gate to the target qubit while leaving the remainder of the memory unaffected. Another way is to apply the gate to its target only
3391:
relies on the adiabatic theorem to undertake calculations. A system is placed in the ground state for a simple
Hamiltonian, which slowly evolves to a more complicated Hamiltonian whose ground state represents the solution to the problem in question. The adiabatic theorem states that if the evolution
3363:
For problems with all these properties, the running time of Grover's algorithm on a quantum computer scales as the square root of the number of inputs (or elements in the database), as opposed to the linear scaling of classical algorithms. A general class of problems to which Grover's algorithm can
2960:
However, quantum computing also poses challenges to traditional cryptographic systems. Shor's algorithm, a quantum algorithm for integer factorization, could potentially break widely used public-key cryptography schemes like RSA, which rely on the difficulty of factoring large numbers. Post-quantum
3341:
queries required for classical algorithms. In this case, the advantage is not only provable but also optimal: it has been shown that Grover's algorithm gives the maximal possible probability of finding the desired element for any number of oracle lookups. Many examples of provable quantum speedups
2956:
Quantum computing has significant potential applications in the fields of cryptography and cybersecurity. Quantum cryptography, which relies on the principles of quantum mechanics, offers the possibility of secure communication channels that are resistant to eavesdropping. Quantum key distribution
3775:
In particular, building computers with large numbers of qubits may be futile if those qubits are not connected well enough and cannot maintain sufficiently high degree of entanglement for long time. When trying to outperform conventional computers, quantum computing researchers often look for new
3722:
spotlight article summarised current quantum computers as being "For now, absolutely nothing". The article elaborated that quantum computers are yet to be more useful or efficient than conventional computers in any case, though it also argued that in the long term such computers are likely to be
3727:
article found that current quantum computing algorithms are "insufficient for practical quantum advantage without significant improvements across the software/hardware stack". It argues that the most promising candidates for achieving speedup with quantum computers are "small-data problems", for
2703:
is the heuristic that quantum computers can be thought of as evaluating a function for multiple input values simultaneously. This can be achieved by preparing a quantum system in a superposition of input states, and applying a unitary transformation that encodes the function to be evaluated. The
3600:
Meeting this scalability condition is possible for a wide range of systems. However, the use of error correction brings with it the cost of a greatly increased number of required qubits. The number required to factor integers using Shor's algorithm is still polynomial, and thought to be between
2964:
Ongoing research in quantum cryptography and post-quantum cryptography is crucial for ensuring the security of communication and data in the face of evolving quantum computing capabilities. Advances in these fields, such as the development of new QKD protocols, the improvement of QRNGs, and the
2411:
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and prototype general purpose machines with up to 20 qubits have been realized. However the technology behind these devices combines complex vacuum equipment, lasers, microwave and radio frequency equipment making full scale processors difficult to integrate with standard computing equipment.
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provide speedup over conventional algorithms only for some tasks, and matching these tasks with practical applications proved challenging. Some promising tasks and applications require resources far beyond those available today. In particular, processing large amounts of non-quantum data is a
6485:
Pirandola, S.; Andersen, U. L.; Banchi, L.; Berta, M.; Bunandar, D.; Colbeck, R.; Englund, D.; Gehring, T.; Lupo, C.; Ottaviani, C.; Pereira, J.; Razavi, M.; Shamsul Shaari, J.; Tomamichel, M.; Usenko, V. C.; Vallone, G.; Villoresi, P.; Wallden, P. (2020). "Advances in quantum cryptography".
2957:(QKD) protocols, such as BB84, enable the secure exchange of cryptographic keys between parties, ensuring the confidentiality and integrity of communication. Moreover, quantum random number generators (QRNGs) can produce high-quality random numbers, which are essential for secure encryption.
3709:
provided direct verification of quantum supremacy experiments by computing exact amplitudes for experimentally generated bitstrings using a new-generation Sunway supercomputer, demonstrating a significant leap in simulation capability built on a multiple-amplitude tensor network contraction
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As of 2023, classical computers outperform quantum computers for all real-world applications. While current quantum computers may speed up solutions to particular mathematical problems, they give no computational advantage for practical tasks. Scientists and engineers are exploring multiple
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million physical qubits would factor 2,048-bit integer in 5 months on a fully error-corrected trapped-ion quantum computer. In terms of the number of physical qubits, to date, this remains the lowest estimate for practically useful integer factorization problem sizing 1,024-bit or larger.
2904:. They both construct a system (a circuit) that represents the physical problem at hand, and then leverage their respective physics properties of the system to seek the âminimumâ. Neuromorphic quantum computing and quantum computing share similar physical properties during computation.
3810:"So the number of continuous parameters describing the state of such a useful quantum computer at any given moment must be... about 10... Could we ever learn to control the more than 10 continuously variable parameters defining the quantum state of such a system? My answer is simple.
768:
is used to refer to an abstract mathematical model and to any physical system that is represented by that model. A classical bit, by definition, exists in either of two physical states, which can be denoted 0 and 1. A qubit is also described by a state, and two states often written
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Conversely, any problem solvable by a quantum computer is also solvable by a classical computer. It is possible to simulate both quantum and classical computers manually with just some paper and a pen, if given enough time. More formally, any quantum computer can be simulated by a
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Bluvstein, Dolev; Evered, Simon J.; Geim, Alexandra A.; Li, Sophie H.; Zhou, Hengyun; Manovitz, Tom; Ebadi, Sepehr; Cain, Madelyn; Kalinowski, Marcin; Hangleiter, Dominik; Ataides, J. Pablo
Bonilla; Maskara, Nishad; Cong, Iris; Gao, Xun; Rodriguez, Pedro Sales (6 December 2023).
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to describe the engineering feat of demonstrating that a programmable quantum device can solve a problem beyond the capabilities of state-of-the-art classical computers. The problem need not be useful, so some view the quantum supremacy test only as a potential future benchmark.
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devices and have scaled to 2000 qubits. However the error rates for larger machines have been on the order of 5%. Technologically these devices are all cryogenic and scaling to large numbers of qubits requires wafer-scale integration, a serious engineering challenge by itself.
176:
shows that some quantum algorithms are exponentially more efficient than the best known classical algorithms. A large-scale quantum computer could in theory solve computational problems unsolvable by a classical computer in any reasonable amount of time. While claims of such
6726:
Guo, Xueshi; Breum, Casper R.; Borregaard, Johannes; Izumi, Shuro; Larsen, Mikkel V.; Gehring, Tobias; Christandl, Matthias; Neergaard-Nielsen, Jonas S.; Andersen, Ulrik L. (23 December 2019). "Distributed quantum sensing in a continuous-variable entangled network".
6531:
Pirandola, S.; Andersen, U. L.; Banchi, L.; Berta, M.; Bunandar, D.; Colbeck, R.; Englund, D.; Gehring, T.; Lupo, C.; Ottaviani, C.; Pereira, J. L.; Razavi, M.; Shamsul Shaari, J.; Tomamichel, M.; Usenko, V. C. (14 December 2020). "Advances in quantum cryptography".
464:
With focus on business managementâs point of view, the potential applications of quantum computing into four major categories are cybersecurity, data analytics and artificial intelligence, optimization and simulation, and data management and searching.
2276:{\displaystyle |00\rangle :={\begin{pmatrix}1\\0\\0\\0\end{pmatrix}};\quad |01\rangle :={\begin{pmatrix}0\\1\\0\\0\end{pmatrix}};\quad |10\rangle :={\begin{pmatrix}0\\0\\1\\0\end{pmatrix}};\quad |11\rangle :={\begin{pmatrix}0\\0\\0\\1\end{pmatrix}}.}
3919:
While quantum computers cannot solve any problems that classical computers cannot already solve, it is suspected that they can solve certain problems faster than classical computers. For instance, it is known that quantum computers can efficiently
3699:, to demonstrate quantum supremacy. The authors claim that a classical contemporary supercomputer would require a computational time of 600 million years to generate the number of samples their quantum processor can generate in 20 seconds.
2290:
2753:. A quantum computation can be described as a network of quantum logic gates and measurements. However, any measurement can be deferred to the end of quantum computation, though this deferment may come at a computational cost, so most
472:
University successfully created "quantum circuits" that correct errors more efficiently than alternative methods, which may potentially remove a major obstacle to practical quantum computers. The
Harvard research team was supported by
3410:
Since quantum computers can produce outputs that classical computers cannot produce efficiently, and since quantum computation is fundamentally linear algebraic, some express hope in developing quantum algorithms that can speed up
4163:; that is, it is believed that there are efficiently checkable problems that are not efficiently solvable by a quantum computer. As a direct consequence of this belief, it is also suspected that BQP is disjoint from the class of
3780:
demonstrations. Therefore, it is desirable to prove lower bounds on the complexity of best possible non-quantum algorithms (which may be unknown) and show that some quantum algorithms asymptomatically improve upon those bounds.
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9644:
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solvable by a classical computer is also solvable by a quantum computer. Intuitively, this is because it is believed that all physical phenomena, including the operation of classical computers, can be described using
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Complexity analysis of algorithms sometimes makes abstract assumptions that do not hold in applications. For example, input data may not already be available encoded in quantum states, and "oracle functions" used in
615:
A classical computer is a quantum computer ... so we shouldn't be asking about "where do quantum speedups come from?" We should say, "well, all computers are quantum. ... Where do classical slowdowns come
3422:, named after its discoverers Harrow, Hassidim, and Lloyd, is believed to provide speedup over classical counterparts. Some research groups have recently explored the use of quantum annealing hardware for training
3099:, give polynomial speedups over corresponding classical algorithms. Though these algorithms give comparably modest quadratic speedup, they are widely applicable and thus give speedups for a wide range of problems.
3005:
can transmit quantum information over relatively short distances. Ongoing experimental research aims to develop more reliable hardware (such as quantum repeaters), hoping to scale this technology to long-distance
1931:
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algorithms could be broken. These are used to protect secure Web pages, encrypted email, and many other types of data. Breaking these would have significant ramifications for electronic privacy and security.
2961:
cryptography, which involves the development of cryptographic algorithms that are resistant to attacks by both classical and quantum computers, is an active area of research aimed at addressing this concern.
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into calculations. National governments have invested heavily in experimental research that aims to develop scalable qubits with longer coherence times and lower error rates. Example implementations include
1608:
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MHz, about 10 seconds. However, the encoding and error-correction overheads increase the size of a real fault-tolerant quantum computer by several orders of magnitude. Careful estimates show that at least
4113:
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In
December 2023, physicists, for the first time, reported the entanglement of individual molecules, which may have significant applications in quantum computing. Also in December 2023, scientists at
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The control of multi-qubit systems requires the generation and coordination of a large number of electrical signals with tight and deterministic timing resolution. This has led to the development of
3578:
As a result, time-consuming tasks may render some quantum algorithms inoperable, as attempting to maintain the state of qubits for a long enough duration will eventually corrupt the superpositions.
3784:
Some researchers have expressed skepticism that scalable quantum computers could ever be built, typically because of the issue of maintaining coherence at large scales, but also for other reasons.
9563:
Liu, Yong; Chen, Yaojian; Guo, Chu; Song, Jiawei; Shi, Xinmin; Gan, Lin; Wu, Wenzhao; Wu, Wei; Fu, Haohuan; Liu, Xin; Chen, Dexun; Zhao, Zhifeng; Yang, Guangwen; Gao, Jiangang (16 January 2024).
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may be an important application of quantum computing. Quantum simulation could also be used to simulate the behavior of atoms and particles at unusual conditions such as the reactions inside a
1296:
1066:
493:'s Optimization with Noisy Intermediate-Scale Quantum devices (ONISQ) program. Research efforts are ongoing to jumpstart quantum computing through topological and photonic approaches as well.
8458:
Amy, Matthew; Matteo, Olivia; Gheorghiu, Vlad; Mosca, Michele; Parent, Alex; Schanck, John (30 November 2016). "Estimating the cost of generic quantum pre-image attacks on SHA-2 and SHA-3".
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A practical quantum computer must use a physical system as a programmable quantum register. Researchers are exploring several technologies as candidates for reliable qubit implementations.
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4161:
3987:
3057:. No mathematical proof has been found that shows that an equally fast classical algorithm cannot be discovered, but evidence suggests that this is unlikely. Certain oracle problems like
1536:
3710:
algorithm. This development underscores the evolving landscape of quantum computing, highlighting both the progress and the complexities involved in validating quantum supremacy claims.
1842:-qubit system is 2-dimensional, and this makes it challenging for a classical computer to simulate a quantum one: representing a 100-qubit system requires storing 2 classical values.
8930:
Pednault, Edwin; Gunnels, John A.; Nannicini, Giacomo; Horesh, Lior; Wisnieff, Robert (22 October 2019). "Leveraging
Secondary Storage to Simulate Deep 54-qubit Sycamore Circuits".
6363:
Aharonov, Dorit; van Dam, Wim; Kempe, Julia; Landau, Zeph; Lloyd, Seth; Regev, Oded (1 January 2008). "Adiabatic
Quantum Computation Is Equivalent to Standard Quantum Computation".
3702:
Claims of quantum supremacy have generated hype around quantum computing, but they are based on contrived benchmark tasks that do not directly imply useful real-world applications.
2028:
1983:
3617:. For a 1000-bit number, this implies a need for about 10 bits without error correction. With error correction, the figure would rise to about 10 bits. Computation time is about
3585:. Error rates are typically proportional to the ratio of operating time to decoherence time, hence any operation must be completed much more quickly than the decoherence time.
2802:
407:. In 1998, a two-qubit quantum computer demonstrated the feasibility of the technology, and subsequent experiments have increased the number of qubits and reduced error rates.
6646:
Xu, Guobin; Mao, Jianzhou; Sakk, Eric; Wang, Shuangbao Paul (22 March 2023). "An
Overview of Quantum-Safe Approaches: Quantum Key Distribution and Post-Quantum Cryptography".
5754:
3563:), typically range between nanoseconds and seconds at low temperature. Currently, some quantum computers require their qubits to be cooled to 20 millikelvin (usually using a
5922:
5456:
Arute, Frank; Arya, Kunal; Babbush, Ryan; Bacon, Dave; Bardin, Joseph C.; et al. (23 October 2019). "Quantum supremacy using a programmable superconducting processor".
5188:
Cao, Yudong; Romero, Jonathan; Olson, Jonathan P.; Degroote, Matthias; Johnson, Peter D.; et al. (9 October 2019). "Quantum
Chemistry in the Age of Quantum Computing".
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shows how increasing the number of qubits can mitigate errors, yet fully fault-tolerant quantum computing remains "a rather distant dream". According to some researchers,
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qubits) can be represented as a network of quantum logic gates from a fairly small family of gates. A choice of gate family that enables this construction is known as a
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with a 54-qubit machine, performing a computation that is impossible for any classical computer. However, the validity of this claim is still being actively researched.
2035:
if another part of the memory is in a desired state. These two choices can be illustrated using another example. The possible states of a two-qubit quantum memory are
2679:
2651:
1450:
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392:
proved that quantum computers could simulate quantum systems without the exponential overhead present in classical simulations, validating
Feynman's 1982 conjecture.
1470:
1217:
1166:
3207:. Some public-key algorithms are based on problems other than the integer factorization and discrete logarithm problems to which Shor's algorithm applies, like the
1018:
3581:
These issues are more difficult for optical approaches as the timescales are orders of magnitude shorter and an often-cited approach to overcoming them is optical
2965:
standardization of post-quantum cryptographic algorithms, will play a key role in maintaining the integrity and confidentiality of information in the quantum era.
7080:
8806:
Boixo, Sergio; Isakov, Sergei V.; Smelyanskiy, Vadim N.; Babbush, Ryan; Ding, Nan; et al. (2018). "Characterizing
Quantum Supremacy in Near-Term Devices".
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tasks that can be solved on quantum computers, but this leaves the possibility that efficient non-quantum techniques will be developed in response, as seen for
3273:
2822:
2994:
does not intercept the message, as any unauthorized eavesdropper would disturb the delicate quantum system and introduce a detectable change. With appropriate
10781:
4577:
Benioff, Paul (1980). "The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines".
164:
In principle, a classical computer can solve the same computational problems as a quantum computer, given enough time. Quantum advantage comes in the form of
7832:
Ajagekar, Akshay; You, Fengqi (5 December 2020). "Quantum computing assisted deep learning for fault detection and diagnosis in industrial process systems".
5823:
3529:
2623:
8994:
Liu, Yong (Alexander); Liu, Xin (Lucy); Li, Fang (Nancy); Fu, Haohuan; Yang, Yuling; et al. (14 November 2021). "Closing the "quantum supremacy" gap".
6909:"Quantum Computing Advance Begins New Era, IBM Says â A quantum computer came up with better answers to a physics problem than a conventional supercomputer"
11179:
Krantz, P.; Kjaergaard, M.; Yan, F.; Orlando, T. P.; Gustavsson, S.; Oliver, W. D. (17 June 2019). "A Quantum Engineer's Guide to Superconducting Qubits".
7031:
9390:
Zhong, Han-Sen; Wang, Hui; Deng, Yu-Hao; Chen, Ming-Cheng; Peng, Li-Chao; et al. (3 December 2020). "Quantum computational advantage using photons".
3672:
In October 2019, Google AI Quantum, with the help of NASA, became the first to claim to have achieved quantum supremacy by performing calculations on the
3121:. In June 2023, IBM computer scientists reported that a quantum computer produced better results for a physics problem than a conventional supercomputer.
3113:
Since chemistry and nanotechnology rely on understanding quantum systems, and such systems are impossible to simulate in an efficient manner classically,
8714:
5728:
2406:{\displaystyle \operatorname {CNOT} :={\begin{pmatrix}1&0&0&0\\0&1&0&0\\0&0&0&1\\0&0&1&0\end{pmatrix}}.}
1874:
13587:
4690:
885:, meaning that they can be multiplied by constants and added together, and the result is again a valid quantum state. Such a combination is known as a
7134:
3226:, which would break many lattice based cryptosystems, is a well-studied open problem. It has been proven that applying Grover's algorithm to break a
3077:
9339:
7934:
Gao, Xun; Anschuetz, Eric R.; Wang, Sheng-Tao; Cirac, J. Ignacio; Lukin, Mikhail D. (2022). "Enhancing Generative Models via Quantum Correlations".
3010:
with end-to-end entanglement. Theoretically, this could enable novel technological applications, such as distributed quantum computing and enhanced
9645:"PsiQuantum Sees 700x Reduction in Computational Resource Requirements to Break Elliptic Curve Cryptography With a Fault Tolerant Quantum Computer"
9261:
4370:
14407:
14140:
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192:
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Biamonte, Jacob; Wittek, Peter; Pancotti, Nicola; Rebentrost, Patrick; Wiebe, Nathan; Lloyd, Seth (September 2017). "Quantum machine learning".
3069:, which is a restricted model where lower bounds are much easier to prove and doesn't necessarily translate to speedups for practical problems.
7783:"Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning"
335:
in 1994. These algorithms did not solve practical problems, but demonstrated mathematically that one could gain more information by querying a
6593:
Xu, Feihu; Ma, Xiongfeng; Zhang, Qiang; Lo, Hoi-Kwong; Pan, Jian-Wei (26 May 2020). "Secure quantum key distribution with realistic devices".
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is slow enough the system will stay in its ground state at all times through the process. Adiabatic optimization may be helpful for solving
3072:
Other problems, including the simulation of quantum physical processes from chemistry and solid-state physics, the approximation of certain
10246:
8879:
9723:
Davies, Paul (6 March 2007). "The implications of a holographic universe for quantum information science and the nature of physical law".
9231:
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Bennett, Charles H.; Bernstein, Ethan; Brassard, Gilles; Vazirani, Umesh (October 1997). "Strengths and Weaknesses of Quantum Computing".
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Conventional computer hardware and algorithms are not only optimized for practical tasks, but are still improving rapidly, particularly
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3613:
is the number of digits in the number to be factored; error correction algorithms would inflate this figure by an additional factor of
635:
14311:
6310:
Raussendorf, Robert; Browne, Daniel E.; Briegel, Hans J. (25 August 2003). "Measurement-based quantum computation on cluster states".
8479:
Dyakonov, M. I. (14 October 2006). S. Luryi; Xu, J.; Zaslavsky, A. (eds.). "Is Fault-Tolerant Quantum Computation Really Possible?".
6424:
Freedman, Michael H.; Larsen, Michael; Wang, Zhenghan (1 June 2002). "A Modular Functor Which is Universal for Quantum Computation".
3935:, for "bounded error, quantum, polynomial time". More formally, BQP is the class of problems that can be solved by a polynomial-time
1541:
5974:
3763:
is used to scale quantum computers to practical applications, its overhead may undermine speedup offered by many quantum algorithms.
297:
to independently suggest that hardware based on quantum phenomena might be more efficient for computer simulation. In a 1984 paper,
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11578:
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3203:
Identifying cryptographic systems that may be secure against quantum algorithms is an actively researched topic under the field of
4328:
meaning. Usually, it means that as a function of input size in bits, the best known classical algorithm for a problem requires an
3163:
systems, is believed to be computationally infeasible with an ordinary computer for large integers if they are the product of few
14323:
11903:
8189:
Pauka SJ, Das K, Kalra B, Moini A, Yang Y, Trainer M, Bousquet A, Cantaloube C, Dick N, Gardner GC, Manfra MJ, Reilly DJ (2021).
3532:
that enable interfacing with the qubits. Scaling these systems to support a growing number of qubits is an additional challenge.
2892:
Neuromorphic quantum computing (abbreviated as ân.quantum computingâ) is an unconventional computing type of computing that uses
601:
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3167:(e.g., products of two 300-digit primes). By comparison, a quantum computer could solve this problem exponentially faster using
82:; however, the current state of the art is largely experimental and impractical, with several obstacles to useful applications.
14007:
13580:
13284:
13256:
3940:
9629:
8596:
Gidney, Craig; EkerÄ, Martin (15 April 2021). "How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits".
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technologies for quantum computing hardware and hope to develop scalable quantum architectures, but serious obstacles remain.
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exist. Quantum algorithms can be roughly categorized by the type of speedup achieved over corresponding classical algorithms.
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Li, Junde; Topaloglu, Rasit; Ghosh, Swaroop (9 January 2021). "Quantum Generative Models for Small Molecule Drug Discovery".
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Chuang, Isaac L.; Gershenfeld, Neil; Kubinec, Markdoi (April 1998). "Experimental Implementation of Fast Quantum Searching".
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Some promising algorithms have been "dequantized", i.e., their non-quantum analogues with similar complexity have been found.
474:
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Investment in quantum computing research has increased in the public and private sectors. As one consulting firm summarized,
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Brassard, Gilles; HĂžyer, Peter; Tapp, Alain (2016). "Quantum Algorithm for the Collision Problem". In Kao, Ming-Yang (ed.).
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Despite high hopes for quantum computing, significant progress in hardware, and optimism about future applications, a 2023
456:... While quantum computing promises to help businesses solve problems that are beyond the reach and speed of conventional
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for finding collisions in two-to-one functions, and Farhi, Goldstone, and Gutmann's algorithm for evaluating NAND trees.
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operations in such a way that the resulting program computes a useful result in theory and is implementable in practice.
281:, which uses quantum theory to describe a simplified computer. When digital computers became faster, physicists faced an
17:
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Rinott, Yosef; Shoham, Tomer; Kalai, Gil (13 July 2021). "Statistical Aspects of the Quantum Supremacy Demonstration".
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through which the algorithm iterates is that of all possible answers. An example and possible application of this is a
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cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations
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Bulmer, Jacob F. F.; Bell, Bryn A.; Chadwick, Rachel S.; Jones, Alex E.; Moise, Diana; et al. (28 January 2022).
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argued that a 400-qubit computer would even come into conflict with the cosmological information bound implied by the
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VepsÀlÀinen, Antti P.; Karamlou, Amir H.; Orrell, John L.; Dogra, Akshunna S.; Loer, Ben; et al. (August 2020).
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are some of the most developed proposals, but experimentalists are considering other hardware possibilities as well.
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In summary, quantum computation can be described as a network of quantum logic gates and measurements. However, any
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Harrow, Aram; Hassidim, Avinatan; Lloyd, Seth (2009). "Quantum algorithm for solving linear systems of equations".
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4803:. IEEE International Conference on Computers, Systems & Signal Processing. Bangalore, India. pp. 175â179.
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4255: â device which can be used to store or transfer information between independent qubits in a quantum computer
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with an error probability of at most 1/3. As a class of probabilistic problems, BQP is the quantum counterpart to
3084:-complete. Because these problems are BQP-complete, an equally fast classical algorithm for them would imply that
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Nayak, Chetan; Simon, Steven; Stern, Ady; Das Sarma, Sankar (2008). "Nonabelian Anyons and Quantum Computation".
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is zero, the qubit is effectively a classical bit; when both are nonzero, the qubit is in superposition. Such a
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13962:
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12859:
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12256:
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3943:("bounded error, probabilistic, polynomial time"), the class of problems that can be solved by polynomial-time
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3179:(in the number of digits of the integer) algorithm for solving the problem. In particular, most of the popular
2825:
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1868:. One important gate for both classical and quantum computation is the NOT gate, which can be represented by a
608:
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model the operations that can be performed on these states. Programming a quantum computer is then a matter of
298:
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5814:"Physicists 'entangle' individual molecules for the first time, hastening possibilities for quantum computing"
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are also not known to be broken by quantum computers, and finding a polynomial time algorithm for solving the
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Pan, Feng; Chen, Keyang; Zhang, Pan (2022). "Solving the Sampling Problem of the Sycamore Quantum Circuits".
5676:
Gibney, Elizabeth (2 October 2019). "Quantum gold rush: the private funding pouring into quantum start-ups".
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Deutsch, D. (8 July 1985). "Quantum theory, the ChurchâTuring principle and the universal quantum computer".
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4187:
4031:, which intuitively would mean that quantum computers are more powerful than classical computers in terms of
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the efficiency of the HaberâBosch process by the mid 2020s although some have predicted it will take longer.
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Quantum algorithms that offer more than a polynomial speedup over the best-known classical algorithm include
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8996:
Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis
5753:
Biondi, Matteo; Heid, Anna; Henke, Nicolaus; Mohr, Niko; Pautasso, Lorenzo; et al. (14 December 2021).
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involves creating procedures that allow a quantum computer to perform calculations efficiently and quickly.
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Physically engineering high-quality qubits has proven challenging. If a physical qubit is not sufficiently
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There exists a boolean function that evaluates each input and determines whether it is the correct answer.
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Information Is Quantum: How Physics Helped Explain the Nature of Information and What Can Be Done With It
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Outeiral, Carlos; Strahm, Martin; Morris, Garrett; Benjamin, Simon; Deane, Charlotte; Shi, Jiye (2021).
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One of the greatest challenges involved with constructing quantum computers is controlling or removing
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Proceedings of the Sixth Annual ACM International Conference on Nanoscale Computing and Communication
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MĂ„rtensson-Pendrill, Ann-Marie (1 November 2006). "The Manhattan projectâa part of physics history".
3914:
3889:. In other words, quantum computers provide no additional power over classical computers in terms of
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Kozlowski, Wojciech; Wehner, Stephanie (25 September 2019). "Towards Large-Scale Quantum Networks".
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2998:, the sender and receiver can thus establish shared private information resistant to eavesdropping.
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for quantum computing, distinguished by the basic elements in which the computation is decomposed.
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to the end of quantum computation, though this deferment may come at a computational cost, so most
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are not necessarily positive numbers. Negative amplitudes allow for destructive wave interference.
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encryption protocols, which drew significant attention to the field of quantum computing. In 1996,
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Benedetti, Marcello; Realpe-GĂłmez, John; Biswas, Rupak; Perdomo-Ortiz, Alejandro (9 August 2016).
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Problems that can be efficiently addressed with Grover's algorithm have the following properties:
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have drawn significant attention to the discipline, near-term practical use cases remain limited.
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There are a number of technical challenges in building a large-scale quantum computer. Physicist
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The number of possible answers to check is the same as the number of inputs to the algorithm, and
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faster than any modern "classical" computer. In particular, a large-scale quantum computer could
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Zu, H.; Dai, W.; de Waele, A.T.A.M. (2022). "Development of Dilution refrigerators â A review".
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Mathematically, the application of such a logic gate to a quantum state vector is modelled with
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IEEE Information Theory Workshop on Theory and Practice in Information-Theoretic Security, 2005
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is impossible to decompose into the tensor product of two individual qubitsâthe two qubits are
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serve as the quantum counterparts of the classical states 0 and 1. However, the quantum states
357:(pictured here in 2017) showed in 1994 that a scalable quantum computer would be able to break
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158:
13808:
9870:
Tacchino, Francesco; Chiesa, Alessandro; Carretta, Stefano; Gerace, Dario (19 December 2019).
9287:
Ball, Philip (3 December 2020). "Physicists in China challenge Google's 'quantum advantage'".
7887:"Quantum computing based hybrid deep learning for fault diagnosis in electrical power systems"
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of its two "basis" states, which loosely means that it is in both states simultaneously. When
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in classical computing. However, unlike a classical bit, which can be in one of two states (a
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10906:; et al. (2003). "Dreams versus Reality: Plenary Debate Session on Quantum Computing".
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Hughes, Ciaran; Isaacson, Joshua; Perry, Anastasia; Sun, Ranbel F.; Turner, Jessica (2021).
9565:"Verifying Quantum Advantage Experiments with Multiple Amplitude Tensor Network Contraction"
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Architecture Framework for Trapped-ion Quantum Computer based on Performance Simulation Tool
8113:
DiVincenzo, David P. (13 April 2000). "The Physical Implementation of Quantum Computation".
5577:
Pan, Feng; Zhang, Pan (4 March 2021). "Simulating the Sycamore quantum supremacy circuits".
2836:. Implementation of Boolean functions using the few-qubit quantum gates is presented here.
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Principles of Quantum Artificial Intelligence: Quantum Problem Solving and Machine Learning
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The most well-known example of a problem that allows for a polynomial quantum speedup is
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Das, A.; Chakrabarti, B. K. (2008). "Quantum Annealing and Analog Quantum Computation".
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5923:"'Off to the races': DARPA, Harvard breakthrough brings quantum computing years closer"
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9872:"Quantum Computers as Universal Quantum Simulators: State-of-the-Art and Perspectives"
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Proceedings of the twenty-fifth annual ACM symposium on Theory of computing â STOC '93
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to find its factors. This ability would allow a quantum computer to break many of the
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5729:"Trump budget proposal boosts funding for artificial intelligence, quantum computing"
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This state of affairs can be traced to several current and long-term considerations.
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investment dollars are pouring in, and quantum-computing start-ups are proliferating.
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of a classical bit. If a quantum computer manipulates the qubit in a particular way,
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8079:"Disentangling Hype from Practicality: On Realistically Achieving Quantum Advantage"
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Preskill, John (26 March 2012). "Quantum computing and the entanglement frontier".
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8539:"Designing a Million-Qubit Quantum Computer Using a Resource Performance Simulator"
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559:
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273:, the fields of quantum mechanics and computer science began to converge. In 1980,
223:
36:
11289:
9262:"Google's 'quantum supremacy' usurped by researchers using ordinary supercomputer"
8998:. SC '21. New York, New York: Association for Computing Machinery. pp. 1â12.
8691:
7394:
5150:
4969:
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number of steps, while a quantum algorithm uses only a polynomial number of steps.
3931:
that can be efficiently solved by a quantum computer with bounded error is called
14285:
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14125:
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11094:
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10190:
10186:
10148:
9837:
8695:
8271:
6807:; Arkhipov, Alex (6 June 2011). "The computational complexity of linear optics".
6624:
4889:
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
4796:
4371:"IBM Quantum Update: Q System One Launch, New Collaborators, and QC Center Plans"
4051:
4032:
3898:
3830:
3522:
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2990:. When a sender and receiver exchange quantum states, they can guarantee that an
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8168:"We'd have more quantum computers if it weren't so hard to find the damn cables"
7206:
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from before) to the second qubit if and only if the first qubit is in the state
265:
applied quantum mechanical models to computational problems and swapped digital
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10644:
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8218:
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8014:
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7817:
7782:
7583:"NSA seeks to build quantum computer that could crack most types of encryption"
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5947:
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Moreover the trapped ion system itself has engineering challenges to overcome.
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10646:
Concise Guide to Quantum Computing: Algorithms, Exercises, and Implementations
10570:
10525:
10500:
10482:
10425:
10407:
10390:
10355:
10302:
10132:
10050:
9366:"The new light-based quantum computer Jiuzhang has achieved quantum supremacy"
8837:
8627:
8420:
7444:
7427:
7353:
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6750:
6266:
6125:
Concise guide to quantum computing: algorithms, exercises, and implementations
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32:
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Online lecture on An Introduction to Quantum Computing, Edward Gerjuoy (2008)
11342:
11220:
11146:"The Quantum Imperative: Addressing the Legal Dimension of Quantum Computers"
10903:
10715:
10699:
10635:
10613:
10583:
10543:
10328:
Benenti, Giuliano; Casati, Giulio; Rossini, Davide; Strini, Giuliano (2019).
10320:
10295:
Elements of Quantum Computing: History, Theories and Engineering Applications
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problem, both of which can be solved by Shor's algorithm. In particular, the
3152:
3133:
3050:
2880:, decomposes computation into a slow continuous transformation of an initial
2857:
2757:
depict a network consisting only of quantum logic gates and no measurements.
2692:
depict a network consisting only of quantum logic gates and no measurements.
593:
242:
for tedious calculations. Both disciplines had practical applications during
169:
98:
10605:
9693:
9421:
9247:
9013:
8964:
6834:
6702:
4641:
3790:
doubted the practicality of quantum computers in a paper published in 1994.
3080:
have quantum algorithms appearing to give super-polynomial speedups and are
3026:
typically focuses on this quantum circuit model, though exceptions like the
66:, and quantum computing leverages this behavior using specialized hardware.
14065:
13678:
13673:
13486:
13145:
12475:
12133:
12058:
11249:. Institute of Electrical and Electronics Engineers Computer Society Press.
10899:
10887:
10330:
Principles of Quantum Computation and Information: A Comprehensive Textbook
9897:
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problems (if an NP-complete problem were in BQP, then it would follow from
3647:
3172:
3164:
2853:
2750:
2735:
1766:
1250:
correspondence between amplitudes and probabilitiesâwhen measuring a qubit
1247:
882:
629:
306:
274:
243:
11359:
Four Lectures on Quantum Computing given at Oxford University in July 2006
10681:
10450:
9701:
9146:
9121:
8191:"A cryogenic CMOS chip for generating control signals for multiple qubits"
8076:
7559:
7507:(29 May 1996). "A fast quantum mechanical algorithm for database search".
7197:
Bernstein, Daniel J. (2009). "Introduction to post-quantum cryptography".
6809:
Proceedings of the forty-third annual ACM symposium on Theory of computing
6455:
5166:
5087:
4951:
3771:
often have internal structure that can be exploited for faster algorithms.
754:
Just as the bit is the basic concept of classical information theory, the
460:, use cases are largely experimental and hypothetical at this early stage.
14103:
13476:
13102:
13014:
12312:
12143:
11997:
11535:
11013:
10945:
10920:
10719:
9729:
9518:"The security implications of quantum cryptography and quantum computing"
8682:
8489:
8127:
7542:
7513:
7385:
7336:
7307:
7290:
7242:
6438:
6377:
6324:
5078:
4846:
4252:
4164:
4042:
The suspected relationship of BQP to several classical complexity classes
3841:
3834:
3791:
3592:, if the error rate is small enough, it is thought to be possible to use
3572:
3488:
993:
539:
12248:
11274:
11031:
10.1002/1521-3978(200009)48:9/11<771::AID-PROP771>3.0.CO;2-E
8145:
10.1002/1521-3978(200009)48:9/11<771::AID-PROP771>3.0.CO;2-E
7780:
7682:
5335:"Hello quantum world! Google publishes landmark quantum supremacy claim"
4991:. Santa Fe, New Mexico, USA: IEEE Comput. Soc. Press. pp. 116â123.
4264: â Application of quantum theory mathematics to cognitive phenomena
3575:
can nevertheless cause certain systems to decohere within milliseconds.
3567:) in order to prevent significant decoherence. A 2020 study argues that
1020:. Because a qubit is a two-state system, any qubit state takes the form
13496:
13426:
13019:
12759:
12615:
12204:
12138:
12002:
11128:
10238:
9676:
9340:"Light-based Quantum Computer Exceeds Fastest Classical Supercomputers"
7602:"The prospects of quantum computing in computational molecular biology"
7504:
6563:
6517:
5247:
5245:
4740:
4598:
3787:
3353:
There is no searchable structure in the collection of possible answers,
1865:
1835:
1786:
389:
365:
354:
309:
protocols and demonstrated that quantum key distribution could enhance
290:
262:
11212:
8537:
Ahsan, Muhammad; Meter, Rodney Van; Kim, Jungsang (28 December 2016).
7628:
7601:
7045:
Ruane, Jonathan; McAfee, Andrew; Oliver, William D. (1 January 2022).
6942:"Evidence for the utility of quantum computing before fault tolerance"
6648:
2023 57th Annual Conference on Information Sciences and Systems (CISS)
6394:
3742:
Current quantum computing hardware generates only a limited amount of
3433:
Deep generative chemistry models emerge as powerful tools to expedite
13957:
13653:
13001:
12962:
11987:
10243:
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
8513:
5399:
3924:, while this is not believed to be the case for classical computers.
3799:
3634:
Another approach to the stability-decoherence problem is to create a
1243:
411:
336:
110:
13565:
10553:
Programming Quantum Computers: Essential Algorithms and Code Samples
8565:
8538:
8362:
8337:
7426:
Farhi, Edward; Goldstone, Jeffrey; Gutmann, Sam (23 December 2008).
6786:
6271:
Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science
5755:"Quantum computing use cases are getting realâwhat you need to know"
5242:
4989:
Proceedings 35th Annual Symposium on Foundations of Computer Science
4620:
Buluta, Iulia; Nori, Franco (2 October 2009). "Quantum Simulators".
4240: â terminology introduced to encompass three classes of methods
3088:
gives a super-polynomial speedup, which is believed to be unlikely.
2884:
into a final Hamiltonian, whose ground states contain the solution.
694:
is a point on the surface of the sphere, partway between the poles,
611:
describes the relationship between quantum and classical computers,
13062:
12552:
12172:
12148:
12007:
11972:
11195:
10837:
10551:
Johnston, Eric R.; Harrigan, Nic; Gimeno-Segovia, Mercedes (2019).
10114:
9888:
9795:
9581:
9404:
9183:
9063:
9004:
8936:
8820:
8773:
8610:
8555:
8464:
8403:
8209:
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7948:
7846:
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6741:
6693:
6607:
6546:
6500:
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5818:
5635:
5583:
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5408:
5202:
4946:. San Diego, California, United States: ACM Press. pp. 11â20.
4809:
4572:
4570:
3514:
3118:
117:
effects can amplify the desired measurement results. The design of
62:
phenomena. On small scales, physical matter exhibits properties of
55:
10746:
10337:
9662:
Unruh, Bill (1995). "Maintaining coherence in Quantum Computers".
8740:
7734:
6825:
6226:
6163:
5388:"Quantum Supremacy Using a Programmable Superconducting Processor"
1926:{\displaystyle X:={\begin{pmatrix}0&1\\1&0\end{pmatrix}}.}
952:
mathematically represents a qubit state. Physicists typically use
12199:
11816:
9956:
9944:
9932:
9920:
9232:"Ordinary computers can beat Google's quantum computer after all"
8880:"Google researchers have reportedly achieved 'quantum supremacy'"
8387:"Impact of ionizing radiation on superconducting qubit coherence"
4168:
3129:
687:{\displaystyle |\psi \rangle =\alpha |0\rangle +\beta |1\rangle }
207:
11090:
Table 1 lists switching and dephasing times for various systems.
9516:
Cavaliere, Fabio; Mattsson, John; Smeets, Ben (September 2020).
7650:
7321:
4689:] (in Russian). Soviet Radio. pp. 13â15. Archived from
4567:
2948:
12176:
11672:
11313:
11262:
11238:"Computing Power into the 21st Century: Moore's Law and Beyond"
9047:"The boundary for quantum advantage in Gaussian boson sampling"
5948:"DARPA-Funded Research Leads to Quantum Computing Breakthrough"
5848:"Logical quantum processor based on reconfigurable atom arrays"
5045:
4834:"Brief history of quantum cryptography: A personal perspective"
3901:, and the existence of quantum computers does not disprove the
3506:
3053:
finite groups. These algorithms depend on the primitive of the
3037:
for factoring and the related quantum algorithms for computing
2760:
Any quantum computation (which is, in the above formalism, any
1603:{\displaystyle 1/{\sqrt {2}}|0\rangle +1/{\sqrt {2}}|1\rangle }
625:
518:. Within these "classical" computers, some components (such as
270:
10999:(2000). "The Physical Implementation of Quantum Computation".
10550:
10443:
Quantum Computation and Information: From Theory to Experiment
8929:
8384:
6856:
6854:
6092:
5129:
Lloyd, Seth (23 August 1996). "Universal Quantum Simulators".
5021:
4801:
Quantum cryptography: Public key distribution and coin tossing
4324:
As used in this article, "exponentially faster" has a precise
3802:
doubt that quantum supremacy will ever be achieved. Physicist
3342:
for query problems are based on Grover's algorithm, including
11445:
10004:
9980:
8805:
7528:
Ambainis, Ambainis (June 2004). "Quantum search algorithms".
5783:"What Business Managers Should Know About Quantum Computing?"
5109:
5107:
4198:
3639:
3501:
Sourcing parts for quantum computers is also very difficult.
2917:
1227:, with one key difference: unlike probabilities, probability
756:
526:) may rely on quantum behavior, but these components are not
490:
437:) machines may have specialized uses in the near future, but
90:
10961:
Berthiaume, Andre (1 December 1998). "Quantum Computation".
10827:
Zeng, Bei; Chen, Xie; Zhou, Duan-Lu; Wen, Xiao-Gang (2019).
9992:
9968:
9869:
8668:; Wang, Zhenghan (2003). "Topological quantum computation".
7599:
7257:"A Public-Key Cryptosystem Based On Algebraic Coding Theory"
7245:
on cryptography not known to be broken by quantum computing.
7175:
6530:
6484:
5975:"Top 7 innovation stories of 2023 â Interesting Engineering"
5591:
5519:"Opinion | Why Google's Quantum Supremacy Milestone Matters"
4770:
3676:
more than 3,000,000 times faster than they could be done on
1864:, analogous to how classical memory can be manipulated with
12194:
11667:
11600:
11348:
Lectures at the Institut Henri Poincaré (slides and videos)
10674:
Quantum Computing: A Short Course from Theory to Experiment
10254:
8077:
Torsten Hoefler; Thomas HĂ€ner; Matthias Troyer (May 2023).
6851:
6651:
6038:
4207:
3380:
with this algorithm is of interest to government agencies.
434:
415:
154:
11178:
10327:
6362:
6034:(Videotape). Event occurs at 1:08:22 – via YouTube.
5104:
4108:{\displaystyle {\mathsf {P\subseteq BQP\subseteq PSPACE}}}
3806:
has expressed skepticism of quantum computing as follows:
11811:
11796:
8953:"IBM casts doubt on Google's claims of quantum supremacy"
8543:
ACM Journal on Emerging Technologies in Computing Systems
3932:
3736:
3556:
3510:
3183:
are based on the difficulty of factoring integers or the
3175:
systems in use today, in the sense that there would be a
3081:
2982:
enables new ways to transmit data securely; for example,
2943:
2598:{\textstyle \operatorname {CNOT} |11\rangle =|10\rangle }
2550:{\textstyle \operatorname {CNOT} |10\rangle =|11\rangle }
2502:{\textstyle \operatorname {CNOT} |01\rangle =|01\rangle }
2454:{\textstyle \operatorname {CNOT} |00\rangle =|00\rangle }
2287:
gate can then be represented using the following matrix:
266:
94:
40:
8656:
7081:"Quantum computing and the chemical industry | McKinsey"
6309:
6211:
5263:
3255:, which involves finding a marked item out of a list of
3124:
About 2% of the annual global energy output is used for
384:
established a quantum speedup for the widely applicable
9515:
9122:"Race Not Over Between Classical and Quantum Computers"
9044:
8457:
7241:, a bibliography maintained by Daniel J. Bernstein and
7238:
6725:
6104:
6080:
6070:
6068:
6055:
6053:
5066:
A fast quantum mechanical algorithm for database search
4203:
Pages displaying short descriptions of redirect targets
2936:. All of these models of computationâquantum circuits,
10886:
10467:
5187:
4388:
3881:, which underlies the operation of quantum computers.
3312:
queries to the database, quadratically fewer than the
2839:
2659:
2631:
2611:
2563:
2515:
2467:
2419:
2305:
2235:
2177:
2119:
2061:
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7933:
7425:
5844:
5455:
4130:
4064:
3995:
3953:
3318:
3285:
3261:
2896:
to perform quantum operations. It was suggested that
2810:
2770:
2293:
2041:
1991:
1946:
1877:
1644:
1616:
1544:
1478:
1458:
1438:
1401:
1373:
1336:
1308:
1256:
1205:
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1026:
1006:
966:
923:
895:
859:
831:
803:
775:
728:
700:
638:
399:
have constructed small-scale quantum computers using
11046:
DiVincenzo, David P. (1995). "Quantum Computation".
9461:"{{subst:title case|Can hype be a force for good?}}"
8481:
Future Trends in Microelectronics. Up the Nano Creek
8240:
DiVincenzo, David P. (1995). "Quantum Computation".
7379:. New York, New York: Springer. pp. 1662â1664.
6065:
6050:
4672:
4294: â Subfield of computer science and mathematics
4270: â Metric for a quantum computer's capabilities
4257:
Pages displaying wikidata descriptions as a fallback
4242:
Pages displaying wikidata descriptions as a fallback
3840:
The first quantum logic gates were implemented with
3481:
Physically scalable to increase the number of qubits
3155:
on cryptographic systems that are currently in use.
3151:
A notable application of quantum computation is for
2749:
decomposes computation into a sequence of few-qubit
93:(or "quantum bit"), serves the same function as the
11638:
8715:"Anyons: The breakthrough quantum computing needs?"
8008:
8006:
8004:
7719:
7428:"A Quantum Algorithm for the Hamiltonian NAND Tree"
6001:"Microsoft Quantum Computing Getting DARPA Funding"
5752:
4522:
2828:, since a computer that can run such circuits is a
8188:
7192:
7190:
6423:
6141:
4155:
4107:
4023:
3981:
3525:cables made only by the Japanese company Coax Co.
3484:Qubits that can be initialized to arbitrary values
3333:
3304:
3267:
2986:uses entangled quantum states to establish secure
2816:
2796:
2673:
2645:
2617:
2597:
2549:
2501:
2453:
2413:As a mathematical consequence of this definition,
2405:
2275:
2022:
1977:
1925:
1658:
1630:
1602:
1530:
1464:
1444:
1424:
1387:
1359:
1322:
1291:{\displaystyle \alpha |0\rangle +\beta |1\rangle }
1290:
1211:
1191:
1160:
1140:
1116:
1088:
1061:{\displaystyle \alpha |0\rangle +\beta |1\rangle }
1060:
1012:
980:
937:
909:
873:
845:
817:
789:
742:
714:
686:
10616:; Shen, Alexander H.; Vyalyi, Mikhail N. (2002).
10577:
10104:
10022:
9962:
9950:
9938:
9926:
9788:
9389:
7885:Ajagekar, Akshay; You, Fengqi (1 December 2021).
7581:Rich, Steven; Gellman, Barton (1 February 2014).
7374:
7044:
5386:Martinis, John; Boixo, Sergio (23 October 2019).
5251:
5051:
4937:
4249: â Computer that uses photons or light waves
3893:. This means that quantum computers cannot solve
3078:quantum algorithm for linear systems of equations
3065:do give provable speedups, though this is in the
2887:
496:
14359:
10706:
10642:
10612:
10109:. Washington, DC: The National Academies Press.
8233:
8001:
7986:
7030:: CS1 maint: bot: original URL status unknown (
7012:. Archived from the original on 15 February 2021
6803:
6122:
5124:
5122:
5033:
4276: â Unintuitive aspects of quantum mechanics
4216: â New technologies actively in development
3102:
2907:
11393:
10826:
10783:Introduction to Classical and Quantum Computing
10441:Hiroshi, Imai; Masahito, Hayashi, eds. (2006).
10440:
10105:Grumbling, Emily; Horowitz, Mark, eds. (2019).
7201:. Berlin, Heidelberg: Springer. pp. 1â14.
7187:
6682:
5612:
5610:
5608:
5606:
4791:
2856:applied to a highly entangled initial state (a
2605:. In other words, the CNOT applies a NOT gate (
193:Timeline of quantum computing and communication
9562:
8757:"Quantum Computing in the NISQ era and beyond"
6939:
6147:
5619:"Quantum Computing in the NISQ era and beyond"
4234: â Computing for the purpose of computing
3231:has against classical brute-force search (see
2867:
13581:
12592:Note: This template roughly follows the 2012
12568:
12264:
11379:
11097:(1982). "Simulating physics with computers".
10185:
10010:
9998:
9986:
9974:
8670:Bulletin of the American Mathematical Society
8536:
8292:
7288:
7181:
7108:"Chemistry is quantum computing's killer app"
7079:Budde, Florian; Volz, Daniel (12 July 2019).
6860:
6645:
6205:
6127:. Texts in computer science. Cham: Springer.
6098:
6044:
5920:
5805:
5597:
5385:
5380:
5378:
5119:
5113:
5027:
4840:. Awaji Island, Japan: IEEE. pp. 19â23.
4776:
4024:{\displaystyle {\mathsf {BQP\subsetneq BPP}}}
11099:International Journal of Theoretical Physics
10445:. Topics in Applied Physics. Vol. 102.
10247:Symposium on Foundations of Computer Science
9168:
8015:"Quantum computers: what are they good for?"
7315:
7291:"Dihedral Hidden Subgroup Problem: A Survey"
6940:Kim, Youngseok; et al. (14 June 2023).
6933:
6900:
6264:
5921:Freedberg Jr., Sydney J. (7 December 2023).
5603:
4721:International Journal of Theoretical Physics
4156:{\displaystyle {\mathsf {NP\nsubseteq BQP}}}
3982:{\displaystyle {\mathsf {BPP\subseteq BQP}}}
3848:The largest commercial systems are based on
3376:that attempts to guess a password. Breaking
3140:
2916:decomposes computation into the braiding of
2668:
2640:
2592:
2578:
2544:
2530:
2496:
2482:
2448:
2434:
2224:
2166:
2108:
2050:
2017:
2003:
1972:
1958:
1653:
1625:
1597:
1568:
1531:{\displaystyle |\alpha |^{2}+|\beta |^{2}=1}
1382:
1317:
1285:
1268:
1111:
1083:
1055:
1038:
975:
932:
904:
868:
840:
812:
784:
737:
709:
681:
664:
647:
250:, and quantum physics was essential for the
238:emerged in the following decades to replace
10671:
10643:Kurgalin, Sergei; Borzunov, Sergei (2021).
10196:Quantum Computation and Quantum Information
8906:"Google and NASA Achieve Quantum Supremacy"
8861:"Quantum Computers Compete for "Supremacy""
8595:
7884:
7831:
7580:
6592:
6123:Kurgalin, Sergei; Borzunov, Sergei (2021).
5781:Leong, Kelvin; Sung, Anna (November 2022).
4306: â Experimental area in semiconductors
4300: â Computing by new or unusual methods
4288: â Type of extremely powerful computer
4222: â List of quantum computer components
3275:items in a database. This can be solved by
441:in quantum gates limits their reliability.
13588:
13574:
12575:
12561:
12535:
12271:
12257:
11386:
11372:
11045:
10995:
10960:
10712:Quantum Mechanics: The Theoretical Minimum
10023:Bernstein, Ethan; Vazirani, Umesh (1997).
8993:
8239:
8112:
5375:
4938:Bernstein, Ethan; Vazirani, Umesh (1993).
4619:
4282: â American quantum computing company
4184: â Canadian quantum computing company
2848:decomposes computation into a sequence of
1765:. This vector inhabits a four-dimensional
568:, in contrast, rely on precise control of
12278:
11194:
11161:
11118:
11067:
11012:
10919:
10836:
10471:Quantum Computing for the Quantum Curious
10370:
10153:Quantum Computer Science: An Introduction
10107:Quantum Computing: Progress and Prospects
10040:
10016:
9887:
9794:
9728:
9675:
9580:
9476:
9403:
9182:
9145:
9119:
9096:
9062:
9003:
8935:
8819:
8790:
8772:
8739:
8681:
8609:
8564:
8554:
8488:
8463:
8402:
8361:
8261:
8208:
8126:
8038:
7992:
7947:
7910:
7845:
7816:
7798:
7733:
7664:
7627:
7617:
7541:
7512:
7443:
7384:
7335:
7306:
7196:
7078:
6975:
6894:"What Can We Do with a Quantum Computer?"
6824:
6740:
6692:
6606:
6545:
6499:
6437:
6376:
6323:
6225:
6180:
6162:
5972:
5889:
5863:
5780:
5727:Rodrigo, Chris Mills (12 February 2020).
5652:
5634:
5582:
5469:
5407:
5358:
5201:
5077:
4845:
4808:
4210: â US information technology company
2923:
2734:A quantum circuit diagram implementing a
1834:because their probability amplitudes are
1432:. Any valid qubit state has coefficients
11235:
10829:Quantum Information Meets Quantum Matter
10066:
9835:
9809:
9458:
8754:
8733:
8478:
8091:
7527:
7474:
7254:
7047:"Quantum Computing for Business Leaders"
6891:
6086:
5616:
5576:
5550:
5516:
5068:. ACM symposium on Theory of computing.
4831:
4825:
4394:
4058:is not known. However, it is known that
4037:
3818:
3597:10, assuming the noise is depolarizing.
3444:
2952:Example of a quantum cryptosystem layout
2947:
2729:
624:
349:
197:
31:
11904:Continuous-variable quantum information
11292:" by Amit Hagar and Michael E. Cuffaro.
11143:
11093:
10736:
10672:Stolze, Joachim; Suter, Dieter (2004).
9363:
8903:
8072:
8070:
8068:
8066:
7132:
7105:
6998:
6024:
5726:
4886:
4787:
4785:
4711:
4576:
4456:
4368:
14:
14408:Computer-related introductions in 1980
14360:
13285:Knowledge representation and reasoning
11314:Quantum computing for the very curious
10515:
10400:Quantum Computing: An Applied Approach
10397:
10147:
9810:Dyakonov, Mikhail (15 November 2018).
9722:
9642:
9627:
8858:
8712:
8092:Dyakonov, Mikhail (15 November 2018).
8012:
7503:
7106:Bourzac, Katherine (30 October 2017).
6872:
6784:
6780:
6778:
6776:
6426:Communications in Mathematical Physics
6110:
6074:
6059:
5998:
5973:Choudhury, Rizwan (30 December 2023).
5675:
5332:
5063:
4493:
4406:
4190: â Information storage technology
4148:
4145:
4142:
4136:
4133:
4100:
4097:
4094:
4091:
4088:
4085:
4079:
4076:
4073:
4067:
4016:
4013:
4010:
4004:
4001:
3998:
3974:
3971:
3968:
3962:
3959:
3956:
3705:In January 2024, a study published in
2944:Quantum cryptography and cybersecurity
2707:
2695:
2023:{\displaystyle X|1\rangle =|0\rangle }
1978:{\displaystyle X|0\rangle =|1\rangle }
1838:. In general, the vector space for an
620:
230:developed in the 1920s to explain the
226:formed distinct academic communities.
128:from its environment, it suffers from
27:Technology that uses quantum mechanics
13595:
13569:
13310:Philosophy of artificial intelligence
12556:
12252:
11367:
11247:"On the Power of Quantum Computation"
11244:
10963:Solution Manual for Quantum Mechanics
10292:
9839:Will We Ever Have a Quantum Computer?
9762:
9743:
9661:
9120:McCormick, Katie (10 February 2022).
8877:
8511:
8335:
8165:
7606:WIREs Computational Molecular Science
6906:
6417:
5811:
5791:Journal of Interdisciplinary Sciences
5333:Gibney, Elizabeth (23 October 2019).
5128:
4985:"On the power of quantum computation"
4982:
4678:
4171:that all problems in NP are in BQP).
3947:with bounded error. It is known that
3344:Brassard, HĂžyer, and Tapp's algorithm
1538:. As an example, measuring the qubit
1242:, the result is a classical bit. The
632:representation of a qubit. The state
574:describe these systems mathematically
12636:Energy consumption (Green computing)
12582:
11330:Quantum computing for the determined
10779:
10588:An Introduction to Quantum Computing
10237:
9812:"The Case Against Quantum Computing"
9630:"Quantum Computers and the Universe"
9286:
8094:"The Case Against Quantum Computing"
8063:
7834:Computers & Chemical Engineering
7005:Lunch & Learn: Quantum Computing
6785:Jordan, Stephen (14 October 2022) .
5826:from the original on 8 December 2023
5039:
4782:
4409:"Plurality of WaveâParticle Duality"
3746:before getting overwhelmed by noise.
3653:
3383:
1845:
76:break widely used encryption schemes
13315:Distributed artificial intelligence
12594:ACM Computing Classification System
11286:Stanford Encyclopedia of Philosophy
9836:Dyakonov, Mikhail (24 March 2020).
9383:
9337:
9229:
8950:
8878:Giles, Martin (20 September 2019).
8530:
8505:
7289:Kobayashi, H.; Gall, F. L. (2006).
6817:Association for Computing Machinery
6793:from the original on 29 April 2018.
6773:
5551:Pednault, Edwin (22 October 2019).
5517:Aaronson, Scott (30 October 2019).
5454: • Journal article:
4714:"Simulating Physics with Computers"
4228: â Quantum computing algorithm
3487:Quantum gates that are faster than
3399:
2840:Measurement-based quantum computing
2681:, nothing is done to either qubit.
246:; computers played a major role in
24:
12827:Integrated development environment
10938:10.1023/B:QINP.0000042203.24782.9a
10880:
10280:
10072:Quantum Computing Since Democritus
9746:"Quantum Supremacy and Complexity"
9364:Conover, Emily (3 December 2020).
8904:Tavares, Frank (23 October 2019).
7295:Information and Media Technologies
6873:Norton, Quinn (15 February 2007).
5302:
4201: â American government agency
3825:List of proposed quantum registers
3477:for a practical quantum computer:
3319:
3240:
3159:, which underpins the security of
2846:measurement-based quantum computer
1669:Each additional qubit doubles the
550:, quantum mechanical notions like
25:
14424:
13295:Automated planning and scheduling
12832:Software configuration management
11255:
10618:Classical and Quantum Computation
9459:Roberson, Tara M. (21 May 2020).
8166:Giles, Martin (17 January 2019).
7856:10.1016/j.compchemeng.2020.107119
7477:Explorations in Quantum Computing
6921:from the original on 14 June 2023
6875:"The Father of Quantum Computing"
4369:Russell, John (10 January 2019).
4046:The exact relationship of BQP to
3503:Superconducting quantum computers
3045:, and more generally solving the
2797:{\displaystyle 2^{n}\times 2^{n}}
503:Introduction to quantum mechanics
418:announced that they had achieved
78:and aid physicists in performing
14342:
14341:
13549:
13539:
13530:
13529:
12534:
12233:
12232:
12223:
12222:
11297:"Quantum computation, theory of"
11273:
11261:
10555:. O'Reilly Media, Incorporated.
10518:Quantum Information: An Overview
9863:
9829:
9803:
9782:
9756:
9737:
9716:
9655:
9636:
9621:
9556:
9509:
9452:
9357:
9331:
9280:
9254:
9223:
9162:
9113:
9038:
8987:
8944:
8923:
8897:
8871:
8852:
8799:
8755:Preskill, John (6 August 2018).
8748:
8727:
8706:
8650:
8589:
8472:
8451:
8378:
8338:"Computing: The quantum company"
8329:
8307:10.1016/j.cryogenics.2021.103390
8286:
8182:
8159:
8106:
8085:
7255:McEliece, R. J. (January 1978).
6892:Ambainis, Andris (Spring 2014).
6534:Advances in Optics and Photonics
6488:Advances in Optics and Photonics
5999:Mackie, Kurt (8 February 2024).
5617:Preskill, John (6 August 2018).
4407:Bhatta, Varun S. (10 May 2020).
3861:
3753:challenge for quantum computers.
3646:used as threads, and relying on
3521:research byproduct, and special
3228:symmetric (secret key) algorithm
2968:
1717:represents a two-qubit state, a
1223:acts similarly to a (classical)
431:noisy intermediate-scale quantum
14388:Computational complexity theory
13540:
12943:Computational complexity theory
9465:Public Understanding of Science
8951:Cho, Adrian (23 October 2019).
8013:Brooks, Michael (24 May 2023).
7980:
7927:
7878:
7825:
7774:
7644:
7593:
7574:
7521:
7497:
7468:
7419:
7368:
7282:
7248:
7231:
7142:Designs, Codes and Cryptography
7126:
7099:
7072:
7038:
6992:
6907:Chang, Kenneth (14 June 2023).
6896:. Institute for Advanced Study.
6885:
6866:
6797:
6719:
6676:
6660:10.1109/CISS56502.2023.10089619
6639:
6586:
6524:
6478:
6356:
6303:
6258:
6116:
6018:
5992:
5966:
5940:
5914:
5838:
5774:
5746:
5720:
5669:
5570:
5544:
5510:
5326:
5296:
5257:
5181:
5072:: ACM Press. pp. 212â219.
5057:
4976:
4931:
4880:
4705:
4335:
3497:Qubits that can be read easily.
2215:
2157:
2099:
1860:can be manipulated by applying
530:from their environment, so any
388:search problem. The same year,
234:observed at atomic scales, and
191:For a chronological guide, see
14291:Relativistic quantum mechanics
12734:Network performance evaluation
11278:Learning materials related to
10908:Quantum Information Processing
10373:Quantum Computing for Everyone
10074:. Cambridge University Press.
9744:Regan, K. W. (23 April 2016).
9599:10.1103/PhysRevLett.132.030601
9201:10.1103/PhysRevLett.129.090502
8713:Monroe, Don (1 October 2008).
8336:Jones, Nicola (19 June 2013).
7912:10.1016/j.apenergy.2021.117628
7752:10.1103/PhysRevLett.103.150502
4712:Feynman, Richard (June 1982).
4613:
4579:Journal of Statistical Physics
4516:
4487:
4450:
4400:
4362:
4318:
3535:
3440:
3366:Boolean satisfiability problem
3328:
3322:
3305:{\displaystyle O({\sqrt {n}})}
3299:
3289:
3091:Some quantum algorithms, like
2888:Neuromorphic quantum computing
2661:
2633:
2585:
2571:
2537:
2523:
2489:
2475:
2441:
2427:
2217:
2159:
2101:
2043:
2010:
1996:
1965:
1951:
1646:
1618:
1590:
1561:
1512:
1503:
1489:
1480:
1412:
1403:
1375:
1347:
1338:
1310:
1278:
1261:
1104:
1076:
1048:
1031:
981:{\displaystyle |\psi \rangle }
968:
925:
897:
861:
833:
805:
777:
730:
702:
674:
657:
640:
497:Quantum information processing
218:For many years, the fields of
13:
1:
14269:Quantum statistical mechanics
14046:Quantum differential calculus
13968:Delayed-choice quantum eraser
13751:Symmetry in quantum mechanics
13098:Multimedia information system
13083:Geographic information system
13073:Enterprise information system
12669:Computer systems organization
11899:Adiabatic quantum computation
10991:– via Semantic Scholar.
10620:. American Mathematical Soc.
10199:(10th anniversary ed.).
9963:Grumbling & Horowitz 2019
9951:Grumbling & Horowitz 2019
9939:Grumbling & Horowitz 2019
9927:Grumbling & Horowitz 2019
9876:Advanced Quantum Technologies
9765:"The Quantum Computer Puzzle"
9643:Swayne, Matt (20 June 2023).
9628:Monroe, Don (December 2022).
9534:10.1016/S1353-4858(20)30105-7
9230:Cho, Adrian (2 August 2022).
8692:10.1090/S0273-0979-02-00964-3
7395:10.1007/978-1-4939-2864-4_304
5252:Grumbling & Horowitz 2019
5151:10.1126/science.273.5278.1073
5052:Grumbling & Horowitz 2019
4465:: MIT Press. pp. 3, 46.
4428:10.18520/cs/v118/i9/1365-1374
4356:
4214:List of emerging technologies
4194:Glossary of quantum computing
4188:Electronic quantum holography
3989:and is widely suspected that
3945:probabilistic Turing machines
3908:
3713:
3683:In December 2020, a group at
3464:
3197:elliptic curve DiffieâHellman
3103:Simulation of quantum systems
3017:
2908:Topological quantum computing
2725:
1769:spanned by the basis vectors
1360:{\displaystyle |\alpha |^{2}}
372:for breaking the widely used
14398:Theoretical computer science
13457:Computational social science
13045:Theoretical computer science
12865:Software development process
12641:Electronic design automation
12626:Very Large Scale Integration
11950:Topological quantum computer
11078:10.1126/science.270.5234.255
10286:
9750:Gödel's Lost Letter and P=NP
9632:. Communications of the ACM.
8859:Savage, Neil (5 July 2017).
8272:10.1126/science.270.5234.255
8081:. Communications of the ACM.
6625:10.1103/RevModPhys.92.025002
6267:"Quantum circuit complexity"
4687:Computable and Noncomputable
4459:Computing: A Concise History
4292:Theoretical computer science
3650:to form stable logic gates.
3636:topological quantum computer
3559:technology, also called the
3505:, like those constructed by
2914:topological quantum computer
2860:), using a technique called
1856:The state of this one-qubit
1677:. As an example, the vector
1425:{\displaystyle |\beta |^{2}}
572:quantum systems. Physicists
368:built on these results with
329:BernsteinâVazirani algorithm
7:
14071:Quantum stochastic calculus
14061:Quantum measurement problem
13983:MachâZehnder interferometer
13280:Natural language processing
13068:Information storage systems
12228:Quantum information science
11395:Quantum information science
11302:Encyclopedia of Mathematics
11163:10.5771/2747-5174-2021-1-52
10025:"Quantum Complexity Theory"
7475:Williams, Colin P. (2011).
7207:10.1007/978-3-540-88702-7_1
7114:. American Chemical Society
5290:10.1103/PhysRevLett.80.3408
5212:10.1021/acs.chemrev.8b00803
4940:"Quantum complexity theory"
4856:10.1109/ITWTPI.2005.1543949
4682:Vychislimoe i nevychislimoe
4174:
3455:adiabatic quantum computers
3217:Lattice-based cryptosystems
3028:quantum adiabatic algorithm
2975:Quantum information science
2938:one-way quantum computation
2932:is the quantum analog of a
2868:Adiabatic quantum computing
2686:measurement can be deferred
760:is the fundamental unit of
558:are largely irrelevant for
343:, sometimes referred to as
287:simulating quantum dynamics
204:MachâZehnder interferometer
10:
14429:
13196:Humanâcomputer interaction
13166:Intrusion detection system
13078:Social information systems
13063:Database management system
12518:Thermoacoustic heat engine
11623:quantum gate teleportation
11144:Jeutner, Valentin (2021).
10971:10.1142/9789814541893_0016
10060:
9309:10.1038/d41586-020-03434-7
8219:10.1038/s41928-020-00528-y
8040:10.1038/d41586-023-01692-9
7966:10.1103/PhysRevX.12.021037
7818:10.1103/PhysRevA.94.022308
7377:Encyclopedia of Algorithms
7133:Lenstra, Arjen K. (2000).
6968:10.1038/s41586-023-06096-3
6342:10.1103/PhysRevA.68.022312
6244:10.1103/RevModPhys.80.1083
6191:10.1103/RevModPhys.80.1061
5979:interestingengineering.com
5874:10.1038/s41586-023-06927-3
5698:10.1038/d41586-019-02935-4
5360:10.1038/d41586-019-03213-z
4545:10.1088/0031-9120/41/6/001
4500:Princeton University Press
4220:List of quantum processors
4121:discrete logarithm problem
3912:
3865:
3822:
3621:or about 10 steps and at 1
3403:
3334:{\displaystyle \Omega (n)}
3244:
3144:
3106:
3063:BernsteinâVazirani problem
2972:
2874:adiabatic quantum computer
2862:quantum gate teleportation
2830:universal quantum computer
2711:
1849:
1659:{\displaystyle |1\rangle }
1631:{\displaystyle |0\rangle }
1388:{\displaystyle |1\rangle }
1323:{\displaystyle |0\rangle }
1117:{\displaystyle |1\rangle }
1089:{\displaystyle |0\rangle }
938:{\displaystyle |1\rangle }
910:{\displaystyle |0\rangle }
874:{\displaystyle |1\rangle }
846:{\displaystyle |0\rangle }
818:{\displaystyle |1\rangle }
790:{\displaystyle |0\rangle }
743:{\displaystyle |1\rangle }
715:{\displaystyle |0\rangle }
500:
458:high-performance computers
305:applied quantum theory to
285:increase in overhead when
190:
186:
101:), a qubit can exist in a
89:in quantum computing, the
14337:
14299:
14251:
14131:Quantum complexity theory
14109:Quantum cellular automata
14084:
14016:
13950:
13863:
13827:
13814:Path integral formulation
13781:
13646:
13603:
13525:
13462:Computational engineering
13437:Computational mathematics
13414:
13361:
13323:
13270:
13232:
13194:
13136:
13053:
12999:
12961:
12913:
12850:
12783:
12747:
12704:
12668:
12601:
12590:
12530:
12503:Immersive virtual reality
12463:
12293:
12286:
12218:
12161:
12124:
12090:
12067:
12034:
12025:
11958:
11887:
11825:
11785:
11752:Quantum Fourier transform
11697:
11648:Post-quantum cryptography
11591:Entanglement distillation
11564:
11473:
11401:
11245:Simon, Daniel R. (1994).
10847:10.1007/978-1-4939-9084-9
10737:Wichert, Andreas (2020).
10655:10.1007/978-3-030-65052-0
10526:10.1007/978-0-387-36944-0
10483:10.1007/978-3-030-61601-4
10408:10.1007/978-3-030-83274-2
10371:Bernhardt, Chris (2019).
10303:10.1007/978-3-319-08284-4
10051:10.1137/S0097539796300921
10029:SIAM Journal on Computing
10011:Nielsen & Chuang 2010
9999:Nielsen & Chuang 2010
9987:Nielsen & Chuang 2010
9975:Nielsen & Chuang 2010
8838:10.1038/s41567-018-0124-x
8628:10.22331/q-2021-04-15-433
8421:10.1038/s41586-020-2619-8
7445:10.4086/toc.2008.v004a008
7354:10.1137/s0097539796300933
7324:SIAM Journal on Computing
7199:Post-Quantum Cryptography
7182:Nielsen & Chuang 2010
6861:Nielsen & Chuang 2010
6751:10.1038/s41567-019-0743-x
6595:Reviews of Modern Physics
6265:Chi-Chih Yao, A. (1993).
6214:Reviews of Modern Physics
6099:Nielsen & Chuang 2010
6045:Nielsen & Chuang 2010
5812:Staff (7 December 2023).
5598:Nielsen & Chuang 2010
5488:10.1038/s41586-019-1666-5
5426:10.1038/s41586-019-1666-5
5303:Holton, William Coffeen.
5274:American Physical Society
5114:Nielsen & Chuang 2010
5028:Nielsen & Chuang 2010
4819:10.1016/j.tcs.2014.05.025
4777:Nielsen & Chuang 2010
4498:. Princeton, New Jersey:
4457:Ceruzzi, Paul E. (2012).
3915:Quantum complexity theory
3856:
3725:Communications of the ACM
3693:photonic quantum computer
3674:Sycamore quantum computer
3205:post-quantum cryptography
3147:Post-quantum cryptography
3141:Post-quantum cryptography
3055:quantum Fourier transform
516:classical electrodynamics
514:'s operation in terms of
489:University and funded by
319:then emerged for solving
174:quantum complexity theory
109:a qubit, the result is a
14198:Quantum machine learning
14178:Quantum key distribution
14168:Quantum image processing
14158:Quantum error correction
14008:Wheeler's delayed choice
13472:Computational healthcare
13467:Differentiable computing
13386:Graphics processing unit
12812:Domain-specific language
12681:Computational complexity
12486:Digital scent technology
12238:Quantum mechanics topics
11933:Quantum machine learning
11909:One-way quantum computer
11762:Quantum phase estimation
11663:Quantum key distribution
11596:Monogamy of entanglement
10710:; Friedman, Art (2014).
10398:Hidary, Jack D. (2021).
10263:10.1109/SFCS.1994.365700
10205:10.1017/CBO9780511976667
10161:10.1017/CBO9780511813870
10080:10.1017/CBO9780511979309
9478:10.1177/0963662520923109
8792:10.22331/q-2018-08-06-79
8512:Ahsan, Muhammad (2015).
6279:10.1109/SFCS.1993.366852
5654:10.22331/q-2018-08-06-79
5553:"On 'Quantum Supremacy'"
4997:10.1109/SFCS.1994.365701
4463:Cambridge, Massachusetts
4311:
4298:Unconventional computing
4226:Magic state distillation
3761:quantum error correction
3594:quantum error correction
3406:Quantum machine learning
3161:public key cryptographic
2984:quantum key distribution
2902:von Neumann architecture
2653:. If the first qubit is
1666:with equal probability.
524:random number generators
339:with a quantum state in
153:(which confine a single
64:both particles and waves
39:, a quantum computer by
14114:Quantum finite automata
13447:Computational chemistry
13381:Photograph manipulation
13272:Artificial intelligence
13088:Decision support system
11845:Randomized benchmarking
11707:Amplitude amplification
11332:â 22 video lectures by
11182:Applied Physics Reviews
11001:Fortschritte der Physik
9763:Kalai, Gil (May 2016).
9694:10.1103/PhysRevA.51.992
9569:Physical Review Letters
9422:10.1126/science.abe8770
9248:10.1126/science.ade2364
9171:Physical Review Letters
9014:10.1145/3458817.3487399
8965:10.1126/science.aaz6080
8170:. MIT Technology Review
8115:Fortschritte der Physik
7722:Physical Review Letters
7154:10.1023/A:1008397921377
7051:Harvard Business Review
6835:10.1145/1993636.1993682
6787:"Quantum Algorithm Zoo"
6703:10.1145/3345312.3345497
5313:EncyclopĂŠdia Britannica
5309:Encyclopedia Britannica
5266:Physical Review Letters
5064:Grover, Lov K. (1996).
4642:10.1126/science.1177838
4496:Alan Turing: The Enigma
4494:Hodges, Andrew (2014).
3707:Physical Review Letters
3224:hidden subgroup problem
3097:amplitude amplification
3047:hidden subgroup problem
2996:cryptographic protocols
2850:Bell state measurements
2674:{\textstyle |0\rangle }
2646:{\textstyle |1\rangle }
1445:{\displaystyle \alpha }
1192:{\displaystyle \alpha }
1141:{\displaystyle \alpha }
956:for quantum mechanical
14218:Quantum neural network
13512:Educational technology
13343:Reinforcement learning
13093:Process control system
12991:Computational geometry
12981:Algorithmic efficiency
12976:Analysis of algorithms
12631:Systems on Chip (SoCs)
12508:Magnetic refrigeration
11945:Quantum Turing machine
11938:quantum neural network
11685:Quantum secret sharing
11316:by Andy Matuschak and
11236:Mitchell, Ian (1998).
10516:Jaeger, Gregg (2007).
9898:10.1002/qute.201900052
9081:10.1126/sciadv.abl9236
7087:. McKinsey and Company
5760:McKinsey & Company
4909:10.1098/rspa.1985.0070
4679:Manin, Yu. I. (1980).
4326:complexity theoretical
4157:
4109:
4043:
4025:
3983:
3937:quantum Turing machine
3687:implemented a type of
3457:
3335:
3306:
3269:
3211:based on a problem in
2953:
2930:quantum Turing machine
2924:Quantum Turing machine
2894:neuromorphic computing
2834:Solovay-Kitaev theorem
2818:
2798:
2742:
2718:There are a number of
2675:
2647:
2619:
2599:
2551:
2503:
2455:
2407:
2277:
2024:
1979:
1927:
1660:
1632:
1604:
1532:
1466:
1465:{\displaystyle \beta }
1446:
1426:
1389:
1361:
1324:
1292:
1213:
1212:{\displaystyle \beta }
1193:
1171:probability amplitudes
1162:
1161:{\displaystyle \beta }
1142:
1118:
1090:
1062:
1014:
982:
939:
911:
875:
847:
819:
791:
751:
744:
716:
688:
618:
586:probability amplitudes
462:
362:
279:quantum Turing machine
215:
212:wave-like interference
159:electromagnetic fields
47:
45:superconducting qubits
14373:Models of computation
14243:Quantum teleportation
13771:Waveâparticle duality
13482:Electronic publishing
13452:Computational biology
13442:Computational physics
13338:Unsupervised learning
13252:Distributed computing
13128:Information retrieval
13035:Mathematical analysis
13025:Mathematical software
12915:Theory of computation
12880:Software construction
12870:Requirements analysis
12748:Software organization
12676:Computer architecture
12646:Hardware acceleration
12611:Printed circuit board
12481:Cloak of invisibility
12280:Emerging technologies
12017:Entanglement-assisted
11978:quantum convolutional
11653:Quantum coin flipping
11618:Quantum teleportation
11579:entanglement-assisted
11409:DiVincenzo's criteria
11150:Morals & Machines
10780:Wong, Thomas (2022).
10682:10.1002/9783527617760
10451:10.1007/3-540-33133-6
10293:Akama, Seiki (2014).
9147:10.1103/Physics.15.19
8884:MIT Technology Review
7560:10.1145/992287.992296
6687:. ACM. pp. 1â7.
6456:10.1007/s002200200645
5088:10.1145/237814.237866
4983:Simon, D. R. (1994).
4952:10.1145/167088.167097
4832:Brassard, G. (2005).
4330:exponentially growing
4158:
4117:integer factorization
4110:
4041:
4026:
3984:
3874:computational problem
3866:Further information:
3823:Further information:
3819:Physical realizations
3796:holographic principle
3691:on 76 photons with a
3565:dilution refrigerator
3448:
3394:computational biology
3336:
3307:
3270:
3209:McEliece cryptosystem
3157:Integer factorization
2973:Further information:
2951:
2819:
2799:
2733:
2720:models of computation
2712:Further information:
2676:
2648:
2620:
2600:
2552:
2504:
2456:
2408:
2285:controlled NOT (CNOT)
2278:
2025:
1980:
1935:matrix multiplication
1928:
1866:classical logic gates
1661:
1633:
1610:would produce either
1605:
1533:
1467:
1447:
1427:
1390:
1362:
1325:
1293:
1214:
1194:
1175:which are in general
1163:
1143:
1119:
1091:
1063:
1015:
1013:{\displaystyle \psi }
1000:for a vector labeled
983:
940:
912:
876:
848:
820:
792:
745:
717:
689:
628:
613:
510:typically describe a
446:
353:
232:waveâparticle duality
228:Modern quantum theory
201:
147:electrical resistance
35:
14393:Classes of computers
14378:Quantum cryptography
14274:Quantum field theory
14203:Quantum metamaterial
14148:Quantum cryptography
13878:Consistent histories
13242:Concurrent computing
13214:Ubiquitous computing
13186:Application security
13181:Information security
13010:Discrete mathematics
12986:Randomized algorithm
12938:Computability theory
12923:Model of computation
12895:Software maintenance
12890:Software engineering
12852:Software development
12802:Programming language
12797:Programming paradigm
12714:Network architecture
11828:processor benchmarks
11757:Quantum optimization
11640:Quantum cryptography
11451:physical vs. logical
11270:at Wikimedia Commons
10997:DiVincenzo, David P.
10965:. pp. 233â234.
10257:. pp. 124â134.
10251:Santa Fe, New Mexico
8658:Freedman, Michael H.
7483:. pp. 242â244.
7308:10.2197/ipsjdc.1.470
7020:– via YouTube.
7002:(21 November 2018).
6819:. pp. 333â342.
6813:San Jose, California
6273:. pp. 352â361.
4128:
4062:
3993:
3951:
3903:ChurchâTuring thesis
3895:undecidable problems
3868:Computability theory
3588:As described by the
3428:deep neural networks
3316:
3283:
3259:
3086:no quantum algorithm
3022:Progress in finding
2980:Quantum cryptography
2808:
2768:
2740:more primitive gates
2657:
2629:
2609:
2561:
2513:
2465:
2417:
2291:
2039:
1989:
1944:
1875:
1642:
1614:
1542:
1476:
1456:
1436:
1399:
1371:
1334:
1306:
1254:
1221:quantum state vector
1203:
1183:
1152:
1132:
1100:
1072:
1024:
1004:
964:
921:
893:
857:
829:
801:
773:
726:
698:
636:
548:randomized algorithm
311:information security
248:wartime cryptography
111:probabilistic output
80:physical simulations
14259:Quantum fluctuation
14228:Quantum programming
14188:Quantum logic gates
14173:Quantum information
14153:Quantum electronics
13628:Classical mechanics
13517:Document management
13507:Operations research
13432:Enterprise software
13348:Multi-task learning
13333:Supervised learning
13055:Information systems
12885:Software deployment
12842:Software repository
12696:Real-time computing
12513:Phased-array optics
12471:Acoustic levitation
11541:Quantum speed limit
11436:Quantum programming
11431:Quantum information
11205:2019ApPRv...6b1318K
11111:1982IJTP...21..467F
11060:1995Sci...270..255D
11023:2000ForPh..48..771D
10930:2003QuIP....2..449A
10892:Doering, Charles R.
9686:1995PhRvA..51..992U
9649:The Quanrum Insider
9591:2024PhRvL.132c0601L
9414:2020Sci...370.1460Z
9398:(6523): 1460â1463.
9344:Scientific American
9301:2020Natur.588..380B
9193:2022PhRvL.129i0502P
9138:2022PhyOJ..15...19M
9073:2022SciA....8.9236B
8865:Scientific American
8830:2018NatPh..14..595B
8783:2018Quant...2...79P
8620:2021Quant...5..433G
8499:2006quant.ph.10117D
8413:2020Natur.584..551V
8354:2013Natur.498..286J
8254:1995Sci...270..255D
8137:2000ForPh..48..771D
8031:2023Natur.617S...1B
7958:2022PhRvX..12b1037G
7903:2021ApEn..30317628A
7809:2016PhRvA..94b2308B
7744:2009PhRvL.103o0502H
7683:10.1038/nature23474
7675:2017Natur.549..195B
7587:The Washington Post
7552:2005quant.ph..4012A
7432:Theory of Computing
7346:1997quant.ph..1001B
7276:1978DSNPR..44..114M
7135:"Integer Factoring"
6960:2023Natur.618..500K
6617:2020RvMP...92b5002X
6601:(2): 025002-3.
6556:2020AdOP...12.1012P
6510:2020AdOP...12.1012P
6448:2002CMaPh.227..605F
6387:2008SIAMR..50..755A
6334:2003PhRvA..68b2312R
6236:2008RvMP...80.1083N
6173:2008RvMP...80.1061D
5690:2019Natur.574...22G
5645:2018Quant...2...79P
5480:2019Natur.574..505A
5418:2019Natur.574..505A
5351:2019Natur.574..461G
5282:1998PhRvL..80.3408C
5254:, pp. 164â169.
5196:(19): 10856â10915.
5143:1996Sci...273.1073L
5137:(5278): 1073â1078.
4901:1985RSPSA.400...97D
4793:Bennett, Charles H.
4733:1982IJTP...21..467F
4634:2009Sci...326..108B
4591:1980JSP....22..563B
4537:2006PhyEd..41..493M
4347:computational basis
3542:quantum decoherence
3530:quantum controllers
3253:unstructured search
3067:quantum query model
3039:discrete logarithms
2714:Quantum programming
2708:Quantum programming
2701:Quantum parallelism
2696:Quantum parallelism
1862:quantum logic gates
1852:Unitarity (physics)
762:quantum information
621:Quantum information
532:quantum information
345:quantum parallelism
325:Deutsch's algorithm
130:quantum decoherence
87:unit of information
18:Quantum computation
14383:Information theory
14312:in popular culture
14094:Quantum algorithms
13942:Von NeumannâWigner
13922:Objective collapse
13633:Old quantum theory
13300:Search methodology
13247:Parallel computing
13204:Interaction design
13113:Computing platform
13040:Numerical analysis
13030:Information theory
12822:Software framework
12785:Software notations
12724:Network components
12621:Integrated circuit
12190:Forest/Rigetti QCS
11926:quantum logic gate
11712:BernsteinâVazirani
11699:Quantum algorithms
11574:Classical capacity
11458:Quantum processors
11441:Quantum simulation
11129:10.1007/BF02650179
10814:on 29 January 2022
10614:Kitaev, Alexei Yu.
9772:Notices of the AMS
8666:Larsen, Michael J.
8196:Nature Electronics
6914:The New York Times
6564:10.1364/AOP.361502
6518:10.1364/AOP.361502
5523:The New York Times
5305:"quantum computer"
4741:10.1007/BF02650179
4599:10.1007/bf01011339
4153:
4105:
4044:
4021:
3979:
3769:Grover's algorithm
3750:Quantum algorithms
3569:ionizing radiation
3494:Universal gate set
3475:these requirements
3458:
3424:Boltzmann machines
3331:
3302:
3277:Grover's algorithm
3265:
3247:Grover's algorithm
3185:discrete logarithm
3181:public key ciphers
3115:quantum simulation
3109:Quantum simulation
3093:Grover's algorithm
3024:quantum algorithms
3003:fiber-optic cables
2988:cryptographic keys
2954:
2898:quantum algorithms
2826:universal gate set
2814:
2794:
2747:quantum gate array
2743:
2671:
2643:
2615:
2595:
2547:
2499:
2451:
2403:
2394:
2273:
2264:
2206:
2148:
2090:
2020:
1975:
1923:
1914:
1656:
1628:
1600:
1528:
1462:
1442:
1422:
1385:
1357:
1320:
1288:
1225:probability vector
1209:
1189:
1158:
1138:
1114:
1086:
1058:
1010:
978:
948:A two-dimensional
935:
907:
871:
843:
815:
787:
752:
740:
712:
684:
544:probability theory
508:Computer engineers
382:Grover's algorithm
370:his 1994 algorithm
363:
317:Quantum algorithms
216:
143:electrical current
141:(which isolate an
119:quantum algorithms
60:quantum mechanical
48:
43:from 2019 with 20
37:Quantum System One
14368:Quantum computing
14355:
14354:
14329:Quantum mysticism
14307:Schrödinger's cat
14238:Quantum simulator
14208:Quantum metrology
14136:Quantum computing
14099:Quantum amplifier
14076:Quantum spacetime
14041:Quantum cosmology
14031:Quantum chemistry
13746:Scattering theory
13694:Zero-point energy
13689:Degenerate levels
13597:Quantum mechanics
13563:
13562:
13492:Electronic voting
13422:Quantum Computing
13415:Applied computing
13401:Image compression
13171:Hardware security
13161:Security services
13118:Digital marketing
12905:Open-source model
12817:Modeling language
12729:Network scheduler
12550:
12549:
12526:
12525:
12333:complexity theory
12318:cellular automata
12246:
12245:
12157:
12156:
12054:Linear optical QC
11835:Quantum supremacy
11789:complexity theory
11742:Quantum annealing
11693:
11692:
11630:Superdense coding
11419:Quantum computing
11290:Quantum Computing
11280:Quantum computing
11266:Media related to
11213:10.1063/1.5089550
11054:(5234): 255â261.
11007:(9â11): 771â783.
10980:978-981-4541-88-6
10904:Brandt, Howard E.
10896:Caves, Carlton M.
10856:978-1-4939-9084-9
10796:979-8-9855931-0-5
10756:978-981-12-2431-7
10729:978-0-465-08061-8
10708:Susskind, Leonard
10691:978-3-527-61776-0
10664:978-3-030-65052-0
10627:978-0-8218-3229-5
10597:978-0-19-857000-4
10580:Laflamme, Raymond
10562:978-1-4920-3968-6
10535:978-0-387-36944-0
10492:978-3-03-061601-4
10460:978-3-540-33133-9
10417:978-3-03-083274-2
10382:978-0-262-35091-4
10347:978-981-3237-23-0
10312:978-3-319-08284-4
10272:978-0-8186-6580-6
10214:978-0-511-99277-3
10170:978-0-511-34258-5
10124:978-0-309-47970-7
10089:978-0-521-19956-8
9664:Physical Review A
9338:Garisto, Daniel.
9023:978-1-4503-8442-1
8549:(4): 39:1â39:25.
8397:(7822): 551â556.
8348:(7454): 286â288.
8248:(5234): 255â261.
8121:(9â11): 771â783.
7936:Physical Review X
7787:Physical Review A
7659:(7671): 195â202.
7629:10.1002/wcms.1481
7490:978-1-84628-887-6
7404:978-1-4939-2864-4
7216:978-3-540-88701-0
7171:on 10 April 2015.
6954:(7965): 500â505.
6844:978-1-4503-0691-1
6712:978-1-4503-6897-1
6669:978-1-6654-5181-9
6395:10.1137/080734479
6312:Physical Review A
6134:978-3-030-65054-4
6113:, pp. 38â39.
5954:. 6 December 2023
5557:IBM Research Blog
5464:(7779): 505â510.
5345:(7779): 461â462.
5097:978-0-89791-785-8
5006:978-0-8186-6580-6
4961:978-0-89791-591-5
4865:978-0-7803-9491-9
4799:(December 1984).
4758:on 8 January 2019
4628:(5949): 108â111.
4525:Physics Education
4502:. p. xviii.
4472:978-0-262-31038-3
4280:Rigetti Computing
4274:Quantum weirdness
4262:Quantum cognition
4247:Optical computing
4238:Natural computing
3879:quantum mechanics
3778:Quantum supremacy
3665:quantum supremacy
3654:Quantum supremacy
3590:threshold theorem
3418:For example, the
3389:Quantum annealing
3384:Quantum annealing
3378:symmetric ciphers
3297:
3268:{\displaystyle n}
3126:nitrogen fixation
3074:Jones polynomials
2920:in a 2D lattice.
2878:quantum annealing
2852:and single-qubit
2817:{\displaystyle n}
1846:Unitary operators
1587:
1558:
1395:with probability
1330:with probability
1124:are the standard
546:when designing a
427:threshold theorem
420:quantum supremacy
333:Simon's algorithm
256:Manhattan Project
236:digital computers
220:quantum mechanics
180:quantum supremacy
115:wave interference
68:Classical physics
16:(Redirected from
14420:
14345:
14344:
14056:Quantum geometry
14051:Quantum dynamics
13908:Superdeterminism
13804:Matrix mechanics
13659:Braâket notation
13590:
13583:
13576:
13567:
13566:
13553:
13552:
13543:
13542:
13533:
13532:
13353:Cross-validation
13325:Machine learning
13209:Social computing
13176:Network security
12971:Algorithm design
12900:Programming team
12860:Control variable
12837:Software library
12775:Software quality
12770:Operating system
12719:Network protocol
12584:Computer science
12577:
12570:
12563:
12554:
12553:
12538:
12537:
12415:machine learning
12390:key distribution
12375:image processing
12365:error correction
12291:
12290:
12273:
12266:
12259:
12250:
12249:
12236:
12235:
12226:
12225:
12032:
12031:
11962:error correction
11891:computing models
11857:Relaxation times
11747:Quantum counting
11636:
11635:
11584:quantum capacity
11531:No-teleportation
11516:No-communication
11388:
11381:
11374:
11365:
11364:
11310:
11277:
11268:Quantum computer
11265:
11250:
11241:
11232:
11198:
11175:
11165:
11140:
11122:
11105:(6â7): 467â488.
11095:Feynman, Richard
11089:
11071:
11042:
11016:
11014:quant-ph/0002077
10992:
10957:
10923:
10921:quant-ph/0310130
10900:Lidar, Daniel M.
10876:
10840:
10823:
10821:
10819:
10813:
10807:. Archived from
10789:. Rooted Grove.
10788:
10776:
10741:(2nd ed.).
10733:
10703:
10668:
10639:
10609:
10574:
10547:
10512:
10476:
10464:
10437:
10402:(2nd ed.).
10394:
10367:
10332:(2nd ed.).
10324:
10276:
10234:
10187:Nielsen, Michael
10182:
10149:Mermin, N. David
10144:
10101:
10055:
10054:
10044:
10035:(5): 1411â1473.
10020:
10014:
10008:
10002:
9996:
9990:
9984:
9978:
9972:
9966:
9960:
9954:
9948:
9942:
9936:
9930:
9924:
9918:
9917:
9891:
9867:
9861:
9860:
9858:
9856:
9833:
9827:
9826:
9824:
9822:
9807:
9801:
9800:
9798:
9786:
9780:
9779:
9769:
9760:
9754:
9753:
9741:
9735:
9734:
9732:
9730:quant-ph/0703041
9720:
9714:
9713:
9679:
9659:
9653:
9652:
9640:
9634:
9633:
9625:
9619:
9618:
9584:
9560:
9554:
9553:
9522:Network Security
9513:
9507:
9506:
9480:
9456:
9450:
9449:
9407:
9387:
9381:
9380:
9378:
9376:
9361:
9355:
9354:
9352:
9350:
9335:
9329:
9328:
9284:
9278:
9277:
9275:
9273:
9258:
9252:
9251:
9227:
9221:
9220:
9186:
9166:
9160:
9159:
9149:
9117:
9111:
9110:
9100:
9066:
9051:Science Advances
9042:
9036:
9035:
9007:
8991:
8985:
8984:
8948:
8942:
8941:
8939:
8927:
8921:
8920:
8918:
8916:
8901:
8895:
8894:
8892:
8890:
8875:
8869:
8868:
8856:
8850:
8849:
8823:
8803:
8797:
8796:
8794:
8776:
8752:
8746:
8745:
8743:
8731:
8725:
8724:
8710:
8704:
8703:
8685:
8683:quant-ph/0101025
8654:
8648:
8647:
8613:
8593:
8587:
8586:
8568:
8558:
8534:
8528:
8527:
8509:
8503:
8502:
8492:
8490:quant-ph/0610117
8476:
8470:
8469:
8467:
8455:
8449:
8448:
8406:
8382:
8376:
8375:
8365:
8333:
8327:
8326:
8290:
8284:
8283:
8265:
8237:
8231:
8230:
8212:
8186:
8180:
8179:
8177:
8175:
8163:
8157:
8156:
8130:
8128:quant-ph/0002077
8110:
8104:
8103:
8089:
8083:
8082:
8074:
8061:
8060:
8042:
8010:
7999:
7998:
7996:
7984:
7978:
7977:
7951:
7931:
7925:
7924:
7914:
7882:
7876:
7875:
7849:
7829:
7823:
7822:
7820:
7802:
7778:
7772:
7771:
7737:
7717:
7711:
7710:
7668:
7648:
7642:
7641:
7631:
7621:
7597:
7591:
7590:
7578:
7572:
7571:
7545:
7543:quant-ph/0504012
7525:
7519:
7518:
7516:
7514:quant-ph/9605043
7501:
7495:
7494:
7472:
7466:
7465:
7447:
7423:
7417:
7416:
7388:
7386:quant-ph/9705002
7372:
7366:
7365:
7339:
7337:quant-ph/9701001
7330:(5): 1510â1523.
7319:
7313:
7312:
7310:
7286:
7280:
7279:
7261:
7252:
7246:
7235:
7229:
7228:
7194:
7185:
7179:
7173:
7172:
7170:
7164:. Archived from
7148:(2/3): 101â128.
7139:
7130:
7124:
7123:
7121:
7119:
7103:
7097:
7096:
7094:
7092:
7085:www.mckinsey.com
7076:
7070:
7069:
7067:
7065:
7042:
7036:
7035:
7029:
7021:
7019:
7017:
6996:
6990:
6989:
6979:
6937:
6931:
6930:
6928:
6926:
6904:
6898:
6897:
6889:
6883:
6882:
6870:
6864:
6858:
6849:
6848:
6828:
6801:
6795:
6794:
6782:
6771:
6770:
6744:
6723:
6717:
6716:
6696:
6680:
6674:
6673:
6643:
6637:
6636:
6610:
6590:
6584:
6583:
6549:
6528:
6522:
6521:
6503:
6494:(4): 1012â1236.
6482:
6476:
6475:
6441:
6439:quant-ph/0001108
6421:
6415:
6414:
6380:
6378:quant-ph/0405098
6360:
6354:
6353:
6327:
6325:quant-ph/0301052
6307:
6301:
6300:
6262:
6256:
6255:
6229:
6220:(3): 1083â1159.
6209:
6203:
6202:
6184:
6166:
6157:(3): 1061â1081.
6145:
6139:
6138:
6120:
6114:
6108:
6102:
6101:, p. 30â32.
6096:
6090:
6084:
6078:
6072:
6063:
6057:
6048:
6042:
6036:
6035:
6028:(31 July 2020).
6026:Bennett, Charlie
6022:
6016:
6015:
6013:
6011:
5996:
5990:
5989:
5987:
5985:
5970:
5964:
5963:
5961:
5959:
5944:
5938:
5937:
5935:
5933:
5927:Breaking Defense
5918:
5912:
5911:
5893:
5867:
5842:
5836:
5835:
5833:
5831:
5809:
5803:
5802:
5800:
5798:
5787:
5778:
5772:
5771:
5769:
5767:
5750:
5744:
5743:
5741:
5739:
5724:
5718:
5717:
5673:
5667:
5666:
5656:
5638:
5614:
5601:
5595:
5589:
5588:
5586:
5574:
5568:
5567:
5565:
5563:
5548:
5542:
5541:
5539:
5537:
5514:
5508:
5507:
5473:
5452:
5450:
5448:
5411:
5382:
5373:
5372:
5362:
5330:
5324:
5323:
5321:
5319:
5300:
5294:
5293:
5261:
5255:
5249:
5240:
5239:
5205:
5190:Chemical Reviews
5185:
5179:
5178:
5126:
5117:
5111:
5102:
5101:
5081:
5079:quant-ph/9605043
5061:
5055:
5049:
5043:
5037:
5031:
5030:, p. 30-32.
5025:
5019:
5018:
4980:
4974:
4973:
4935:
4929:
4928:
4895:(1818): 97â117.
4884:
4878:
4877:
4849:
4847:quant-ph/0604072
4829:
4823:
4822:
4812:
4797:Brassard, Gilles
4789:
4780:
4774:
4768:
4767:
4765:
4763:
4757:
4751:. Archived from
4727:(6/7): 467â488.
4718:
4709:
4703:
4702:
4700:
4698:
4676:
4670:
4669:
4617:
4611:
4610:
4574:
4565:
4564:
4520:
4514:
4513:
4491:
4485:
4484:
4454:
4448:
4447:
4413:
4404:
4398:
4392:
4386:
4385:
4383:
4381:
4366:
4350:
4339:
4333:
4322:
4258:
4243:
4204:
4162:
4160:
4159:
4154:
4152:
4151:
4114:
4112:
4111:
4106:
4104:
4103:
4030:
4028:
4027:
4022:
4020:
4019:
3988:
3986:
3985:
3980:
3978:
3977:
3804:Mikhail Dyakonov
3798:. Skeptics like
3662:coined the term
3629:
3624:
3471:David DiVincenzo
3413:machine learning
3400:Machine learning
3374:password cracker
3364:be applied is a
3340:
3338:
3337:
3332:
3311:
3309:
3308:
3303:
3298:
3293:
3274:
3272:
3271:
3266:
3169:Shor's algorithm
3035:Shor's algorithm
3008:quantum networks
2823:
2821:
2820:
2815:
2803:
2801:
2800:
2795:
2793:
2792:
2780:
2779:
2755:quantum circuits
2690:quantum circuits
2680:
2678:
2677:
2672:
2664:
2652:
2650:
2649:
2644:
2636:
2624:
2622:
2621:
2616:
2604:
2602:
2601:
2596:
2588:
2574:
2556:
2554:
2553:
2548:
2540:
2526:
2508:
2506:
2505:
2500:
2492:
2478:
2460:
2458:
2457:
2452:
2444:
2430:
2412:
2410:
2409:
2404:
2399:
2398:
2282:
2280:
2279:
2274:
2269:
2268:
2220:
2211:
2210:
2162:
2153:
2152:
2104:
2095:
2094:
2046:
2029:
2027:
2026:
2021:
2013:
1999:
1984:
1982:
1981:
1976:
1968:
1954:
1932:
1930:
1929:
1924:
1919:
1918:
1827:
1826:
1825:|11⟩
1823:
1821:
1820:
1817:
1814:
1807:
1806:|00⟩
1804:
1802:
1801:
1798:
1795:
1784:
1783:|11⟩
1780:
1779:|10⟩
1776:
1775:|01⟩
1772:
1771:|00⟩
1764:
1763:
1760:
1758:
1757:
1754:
1751:
1744:
1741:
1739:
1738:
1735:
1732:
1724:
1716:
1715:
1714:|01⟩
1712:
1710:
1709:
1706:
1703:
1696:
1695:|00⟩
1693:
1691:
1690:
1687:
1684:
1665:
1663:
1662:
1657:
1649:
1637:
1635:
1634:
1629:
1621:
1609:
1607:
1606:
1601:
1593:
1588:
1583:
1581:
1564:
1559:
1554:
1552:
1537:
1535:
1534:
1529:
1521:
1520:
1515:
1506:
1498:
1497:
1492:
1483:
1471:
1469:
1468:
1463:
1451:
1449:
1448:
1443:
1431:
1429:
1428:
1423:
1421:
1420:
1415:
1406:
1394:
1392:
1391:
1386:
1378:
1366:
1364:
1363:
1358:
1356:
1355:
1350:
1341:
1329:
1327:
1326:
1321:
1313:
1297:
1295:
1294:
1289:
1281:
1264:
1234:When a qubit is
1218:
1216:
1215:
1210:
1198:
1196:
1195:
1190:
1167:
1165:
1164:
1159:
1147:
1145:
1144:
1139:
1123:
1121:
1120:
1115:
1107:
1095:
1093:
1092:
1087:
1079:
1067:
1065:
1064:
1059:
1051:
1034:
1019:
1017:
1016:
1011:
999:
996:
990:
987:
985:
984:
979:
971:
944:
942:
941:
936:
928:
916:
914:
913:
908:
900:
880:
878:
877:
872:
864:
852:
850:
849:
844:
836:
824:
822:
821:
816:
808:
796:
794:
793:
788:
780:
764:. The same term
749:
747:
746:
741:
733:
721:
719:
718:
713:
705:
693:
691:
690:
685:
677:
660:
643:
566:Quantum programs
560:program analysis
455:
451:
397:experimentalists
395:Over the years,
224:computer science
52:quantum computer
21:
14428:
14427:
14423:
14422:
14421:
14419:
14418:
14417:
14358:
14357:
14356:
14351:
14333:
14319:Wigner's friend
14295:
14286:Quantum gravity
14247:
14233:Quantum sensing
14213:Quantum network
14193:Quantum machine
14163:Quantum imaging
14126:Quantum circuit
14121:Quantum channel
14080:
14026:Quantum biology
14012:
13988:ElitzurâVaidman
13963:DavissonâGermer
13946:
13898:Hidden-variable
13888:de BroglieâBohm
13865:Interpretations
13859:
13823:
13777:
13664:Complementarity
13642:
13599:
13594:
13564:
13559:
13550:
13521:
13502:Word processing
13410:
13396:Virtual reality
13357:
13319:
13290:Computer vision
13266:
13262:Multiprocessing
13228:
13190:
13156:Security hacker
13132:
13108:Digital library
13049:
13000:Mathematics of
12995:
12957:
12933:Automata theory
12928:Formal language
12909:
12875:Software design
12846:
12779:
12765:Virtual machine
12743:
12739:Network service
12700:
12691:Embedded system
12664:
12597:
12586:
12581:
12551:
12546:
12522:
12459:
12370:finite automata
12282:
12277:
12247:
12242:
12214:
12164:
12153:
12126:Superconducting
12120:
12086:
12077:Neutral atom QC
12069:Ultracold atoms
12063:
12028:implementations
12027:
12021:
11961:
11954:
11921:Quantum circuit
11889:
11883:
11877:
11867:
11827:
11821:
11788:
11781:
11737:Hidden subgroup
11689:
11678:other protocols
11634:
11611:quantum network
11606:Quantum channel
11566:
11560:
11506:No-broadcasting
11496:GottesmanâKnill
11469:
11397:
11392:
11357:Lomonaco, Sam.
11334:Michael Nielsen
11318:Michael Nielsen
11295:
11258:
11253:
11069:10.1.1.242.2165
10981:
10883:
10881:Academic papers
10857:
10817:
10815:
10811:
10797:
10786:
10757:
10730:
10692:
10665:
10628:
10598:
10578:Kaye, Phillip;
10563:
10536:
10493:
10474:
10461:
10418:
10383:
10348:
10313:
10289:
10283:
10281:Further reading
10273:
10215:
10171:
10125:
10090:
10068:Aaronson, Scott
10063:
10058:
10042:10.1.1.144.7852
10021:
10017:
10009:
10005:
9997:
9993:
9985:
9981:
9973:
9969:
9961:
9957:
9949:
9945:
9937:
9933:
9925:
9921:
9868:
9864:
9854:
9852:
9850:
9834:
9830:
9820:
9818:
9808:
9804:
9787:
9783:
9767:
9761:
9757:
9742:
9738:
9721:
9717:
9660:
9656:
9641:
9637:
9626:
9622:
9561:
9557:
9514:
9510:
9457:
9453:
9388:
9384:
9374:
9372:
9362:
9358:
9348:
9346:
9336:
9332:
9285:
9281:
9271:
9269:
9268:. 5 August 2022
9260:
9259:
9255:
9228:
9224:
9167:
9163:
9118:
9114:
9057:(4): eabl9236.
9043:
9039:
9024:
8992:
8988:
8949:
8945:
8928:
8924:
8914:
8912:
8902:
8898:
8888:
8886:
8876:
8872:
8857:
8853:
8804:
8800:
8753:
8749:
8732:
8728:
8711:
8707:
8655:
8651:
8594:
8590:
8566:10.1145/2830570
8535:
8531:
8510:
8506:
8477:
8473:
8456:
8452:
8383:
8379:
8363:10.1038/498286a
8334:
8330:
8291:
8287:
8263:10.1.1.242.2165
8238:
8234:
8187:
8183:
8173:
8171:
8164:
8160:
8111:
8107:
8090:
8086:
8075:
8064:
8025:(7962): S1âS3.
8011:
8002:
7985:
7981:
7932:
7928:
7883:
7879:
7830:
7826:
7779:
7775:
7718:
7714:
7649:
7645:
7598:
7594:
7579:
7575:
7530:ACM SIGACT News
7526:
7522:
7502:
7498:
7491:
7473:
7469:
7424:
7420:
7405:
7373:
7369:
7320:
7316:
7287:
7283:
7259:
7253:
7249:
7236:
7232:
7217:
7195:
7188:
7180:
7176:
7168:
7137:
7131:
7127:
7117:
7115:
7104:
7100:
7090:
7088:
7077:
7073:
7063:
7061:
7043:
7039:
7023:
7022:
7015:
7013:
7000:Morello, Andrea
6997:
6993:
6938:
6934:
6924:
6922:
6905:
6901:
6890:
6886:
6871:
6867:
6859:
6852:
6845:
6805:Aaronson, Scott
6802:
6798:
6783:
6774:
6724:
6720:
6713:
6681:
6677:
6670:
6644:
6640:
6591:
6587:
6529:
6525:
6483:
6479:
6422:
6418:
6361:
6357:
6308:
6304:
6289:
6263:
6259:
6210:
6206:
6182:10.1.1.563.9990
6151:Rev. Mod. Phys.
6146:
6142:
6135:
6121:
6117:
6109:
6105:
6097:
6093:
6085:
6081:
6073:
6066:
6058:
6051:
6043:
6039:
6023:
6019:
6009:
6007:
5997:
5993:
5983:
5981:
5971:
5967:
5957:
5955:
5946:
5945:
5941:
5931:
5929:
5919:
5915:
5858:(7997): 58â65.
5843:
5839:
5829:
5827:
5810:
5806:
5796:
5794:
5785:
5779:
5775:
5765:
5763:
5751:
5747:
5737:
5735:
5725:
5721:
5684:(7776): 22â24.
5674:
5670:
5615:
5604:
5596:
5592:
5575:
5571:
5561:
5559:
5549:
5545:
5535:
5533:
5515:
5511:
5453:
5446:
5444:
5383:
5376:
5331:
5327:
5317:
5315:
5301:
5297:
5262:
5258:
5250:
5243:
5186:
5182:
5127:
5120:
5112:
5105:
5098:
5062:
5058:
5050:
5046:
5038:
5034:
5026:
5022:
5007:
4981:
4977:
4962:
4936:
4932:
4885:
4881:
4866:
4830:
4826:
4790:
4783:
4775:
4771:
4761:
4759:
4755:
4716:
4710:
4706:
4696:
4694:
4677:
4673:
4618:
4614:
4575:
4568:
4521:
4517:
4510:
4492:
4488:
4473:
4455:
4451:
4416:Current Science
4411:
4405:
4401:
4393:
4389:
4379:
4377:
4367:
4363:
4359:
4354:
4353:
4340:
4336:
4323:
4319:
4314:
4309:
4256:
4241:
4202:
4177:
4132:
4131:
4129:
4126:
4125:
4066:
4065:
4063:
4060:
4059:
4033:time complexity
3997:
3996:
3994:
3991:
3990:
3955:
3954:
3952:
3949:
3948:
3922:factor integers
3917:
3911:
3899:halting problem
3870:
3864:
3859:
3831:Superconductors
3827:
3821:
3723:useful. A 2023
3716:
3656:
3644:quasi-particles
3627:
3622:
3550:
3538:
3523:superconducting
3467:
3443:
3408:
3402:
3386:
3317:
3314:
3313:
3292:
3284:
3281:
3280:
3260:
3257:
3256:
3249:
3243:
3241:Search problems
3177:polynomial time
3149:
3143:
3111:
3105:
3059:Simon's problem
3043:Pell's equation
3020:
3012:quantum sensing
2977:
2971:
2946:
2926:
2910:
2890:
2870:
2842:
2809:
2806:
2805:
2788:
2784:
2775:
2771:
2769:
2766:
2765:
2728:
2716:
2710:
2698:
2660:
2658:
2655:
2654:
2632:
2630:
2627:
2626:
2610:
2607:
2606:
2584:
2570:
2562:
2559:
2558:
2536:
2522:
2514:
2511:
2510:
2488:
2474:
2466:
2463:
2462:
2440:
2426:
2418:
2415:
2414:
2393:
2392:
2387:
2382:
2377:
2371:
2370:
2365:
2360:
2355:
2349:
2348:
2343:
2338:
2333:
2327:
2326:
2321:
2316:
2311:
2301:
2300:
2292:
2289:
2288:
2263:
2262:
2256:
2255:
2249:
2248:
2242:
2241:
2231:
2230:
2216:
2205:
2204:
2198:
2197:
2191:
2190:
2184:
2183:
2173:
2172:
2158:
2147:
2146:
2140:
2139:
2133:
2132:
2126:
2125:
2115:
2114:
2100:
2089:
2088:
2082:
2081:
2075:
2074:
2068:
2067:
2057:
2056:
2042:
2040:
2037:
2036:
2009:
1995:
1990:
1987:
1986:
1964:
1950:
1945:
1942:
1941:
1913:
1912:
1907:
1901:
1900:
1895:
1885:
1884:
1876:
1873:
1872:
1854:
1848:
1824:
1818:
1815:
1812:
1811:
1809:
1805:
1799:
1796:
1793:
1792:
1790:
1789:
1782:
1778:
1774:
1770:
1762:|1⟩
1761:
1755:
1752:
1749:
1748:
1746:
1743:|0⟩
1742:
1736:
1733:
1730:
1729:
1727:
1726:
1725:with the qubit
1723:|0⟩
1722:
1713:
1707:
1704:
1701:
1700:
1698:
1694:
1688:
1685:
1682:
1681:
1679:
1678:
1645:
1643:
1640:
1639:
1617:
1615:
1612:
1611:
1589:
1582:
1577:
1560:
1553:
1548:
1543:
1540:
1539:
1516:
1511:
1510:
1502:
1493:
1488:
1487:
1479:
1477:
1474:
1473:
1457:
1454:
1453:
1437:
1434:
1433:
1416:
1411:
1410:
1402:
1400:
1397:
1396:
1374:
1372:
1369:
1368:
1351:
1346:
1345:
1337:
1335:
1332:
1331:
1309:
1307:
1304:
1303:
1277:
1260:
1255:
1252:
1251:
1204:
1201:
1200:
1184:
1181:
1180:
1177:complex numbers
1153:
1150:
1149:
1133:
1130:
1129:
1103:
1101:
1098:
1097:
1075:
1073:
1070:
1069:
1047:
1030:
1025:
1022:
1021:
1005:
1002:
1001:
997:
991:
988:
967:
965:
962:
961:
924:
922:
919:
918:
896:
894:
891:
890:
860:
858:
855:
854:
832:
830:
827:
826:
804:
802:
799:
798:
776:
774:
771:
770:
729:
727:
724:
723:
701:
699:
696:
695:
673:
656:
639:
637:
634:
633:
623:
609:Charlie Bennett
582:Complex numbers
512:modern computer
505:
499:
479:QuEra Computing
453:
449:
405:superconductors
321:oracle problems
303:Gilles Brassard
299:Charles Bennett
295:Richard Feynman
277:introduced the
252:nuclear physics
240:human computers
196:
189:
166:time complexity
155:atomic particle
145:by eliminating
139:superconductors
28:
23:
22:
15:
12:
11:
5:
14426:
14416:
14415:
14413:Supercomputers
14410:
14405:
14400:
14395:
14390:
14385:
14380:
14375:
14370:
14353:
14352:
14350:
14349:
14338:
14335:
14334:
14332:
14331:
14326:
14321:
14316:
14315:
14314:
14303:
14301:
14297:
14296:
14294:
14293:
14288:
14283:
14282:
14281:
14271:
14266:
14264:Casimir effect
14261:
14255:
14253:
14249:
14248:
14246:
14245:
14240:
14235:
14230:
14225:
14223:Quantum optics
14220:
14215:
14210:
14205:
14200:
14195:
14190:
14185:
14180:
14175:
14170:
14165:
14160:
14155:
14150:
14145:
14144:
14143:
14133:
14128:
14123:
14118:
14117:
14116:
14106:
14101:
14096:
14090:
14088:
14082:
14081:
14079:
14078:
14073:
14068:
14063:
14058:
14053:
14048:
14043:
14038:
14033:
14028:
14022:
14020:
14014:
14013:
14011:
14010:
14005:
14000:
13998:Quantum eraser
13995:
13990:
13985:
13980:
13975:
13970:
13965:
13960:
13954:
13952:
13948:
13947:
13945:
13944:
13939:
13934:
13929:
13924:
13919:
13914:
13913:
13912:
13911:
13910:
13895:
13890:
13885:
13880:
13875:
13869:
13867:
13861:
13860:
13858:
13857:
13852:
13847:
13842:
13837:
13831:
13829:
13825:
13824:
13822:
13821:
13816:
13811:
13806:
13801:
13796:
13791:
13785:
13783:
13779:
13778:
13776:
13775:
13774:
13773:
13768:
13758:
13753:
13748:
13743:
13738:
13733:
13728:
13723:
13718:
13713:
13708:
13703:
13698:
13697:
13696:
13691:
13686:
13681:
13671:
13669:Density matrix
13666:
13661:
13656:
13650:
13648:
13644:
13643:
13641:
13640:
13635:
13630:
13625:
13624:
13623:
13613:
13607:
13605:
13601:
13600:
13593:
13592:
13585:
13578:
13570:
13561:
13560:
13558:
13557:
13547:
13537:
13526:
13523:
13522:
13520:
13519:
13514:
13509:
13504:
13499:
13494:
13489:
13484:
13479:
13474:
13469:
13464:
13459:
13454:
13449:
13444:
13439:
13434:
13429:
13424:
13418:
13416:
13412:
13411:
13409:
13408:
13406:Solid modeling
13403:
13398:
13393:
13388:
13383:
13378:
13373:
13367:
13365:
13359:
13358:
13356:
13355:
13350:
13345:
13340:
13335:
13329:
13327:
13321:
13320:
13318:
13317:
13312:
13307:
13305:Control method
13302:
13297:
13292:
13287:
13282:
13276:
13274:
13268:
13267:
13265:
13264:
13259:
13257:Multithreading
13254:
13249:
13244:
13238:
13236:
13230:
13229:
13227:
13226:
13221:
13216:
13211:
13206:
13200:
13198:
13192:
13191:
13189:
13188:
13183:
13178:
13173:
13168:
13163:
13158:
13153:
13151:Formal methods
13148:
13142:
13140:
13134:
13133:
13131:
13130:
13125:
13123:World Wide Web
13120:
13115:
13110:
13105:
13100:
13095:
13090:
13085:
13080:
13075:
13070:
13065:
13059:
13057:
13051:
13050:
13048:
13047:
13042:
13037:
13032:
13027:
13022:
13017:
13012:
13006:
13004:
12997:
12996:
12994:
12993:
12988:
12983:
12978:
12973:
12967:
12965:
12959:
12958:
12956:
12955:
12950:
12945:
12940:
12935:
12930:
12925:
12919:
12917:
12911:
12910:
12908:
12907:
12902:
12897:
12892:
12887:
12882:
12877:
12872:
12867:
12862:
12856:
12854:
12848:
12847:
12845:
12844:
12839:
12834:
12829:
12824:
12819:
12814:
12809:
12804:
12799:
12793:
12791:
12781:
12780:
12778:
12777:
12772:
12767:
12762:
12757:
12751:
12749:
12745:
12744:
12742:
12741:
12736:
12731:
12726:
12721:
12716:
12710:
12708:
12702:
12701:
12699:
12698:
12693:
12688:
12683:
12678:
12672:
12670:
12666:
12665:
12663:
12662:
12653:
12648:
12643:
12638:
12633:
12628:
12623:
12618:
12613:
12607:
12605:
12599:
12598:
12591:
12588:
12587:
12580:
12579:
12572:
12565:
12557:
12548:
12547:
12545:
12544:
12531:
12528:
12527:
12524:
12523:
12521:
12520:
12515:
12510:
12505:
12500:
12499:
12498:
12488:
12483:
12478:
12473:
12467:
12465:
12461:
12460:
12458:
12457:
12452:
12447:
12442:
12437:
12432:
12430:neural network
12427:
12422:
12417:
12412:
12407:
12402:
12397:
12392:
12387:
12382:
12377:
12372:
12367:
12362:
12357:
12352:
12351:
12350:
12340:
12335:
12330:
12325:
12320:
12315:
12310:
12305:
12299:
12297:
12288:
12284:
12283:
12276:
12275:
12268:
12261:
12253:
12244:
12243:
12241:
12240:
12230:
12219:
12216:
12215:
12213:
12212:
12210:many others...
12207:
12202:
12197:
12192:
12183:
12169:
12167:
12159:
12158:
12155:
12154:
12152:
12151:
12146:
12141:
12136:
12130:
12128:
12122:
12121:
12119:
12118:
12113:
12108:
12103:
12097:
12095:
12088:
12087:
12085:
12084:
12082:Trapped-ion QC
12079:
12073:
12071:
12065:
12064:
12062:
12061:
12056:
12051:
12046:
12040:
12038:
12036:Quantum optics
12029:
12023:
12022:
12020:
12019:
12014:
12013:
12012:
12005:
12000:
11995:
11990:
11985:
11980:
11975:
11966:
11964:
11956:
11955:
11953:
11952:
11947:
11942:
11941:
11940:
11930:
11929:
11928:
11918:
11917:
11916:
11906:
11901:
11895:
11893:
11885:
11884:
11882:
11881:
11880:
11879:
11875:
11869:
11865:
11854:
11853:
11852:
11842:
11840:Quantum volume
11837:
11831:
11829:
11823:
11822:
11820:
11819:
11814:
11809:
11804:
11799:
11793:
11791:
11783:
11782:
11780:
11779:
11774:
11769:
11764:
11759:
11754:
11749:
11744:
11739:
11734:
11729:
11724:
11719:
11717:Boson sampling
11714:
11709:
11703:
11701:
11695:
11694:
11691:
11690:
11688:
11687:
11682:
11681:
11680:
11675:
11670:
11660:
11655:
11650:
11644:
11642:
11633:
11632:
11627:
11626:
11625:
11615:
11614:
11613:
11603:
11598:
11593:
11588:
11587:
11586:
11581:
11570:
11568:
11562:
11561:
11559:
11558:
11553:
11551:SolovayâKitaev
11548:
11543:
11538:
11533:
11528:
11523:
11518:
11513:
11508:
11503:
11498:
11493:
11488:
11483:
11477:
11475:
11471:
11470:
11468:
11467:
11466:
11465:
11455:
11454:
11453:
11443:
11438:
11433:
11428:
11427:
11426:
11416:
11411:
11405:
11403:
11399:
11398:
11391:
11390:
11383:
11376:
11368:
11362:
11361:
11355:
11350:
11345:
11339:Video Lectures
11336:
11326:
11325:
11321:
11320:
11311:
11293:
11283:
11282:at Wikiversity
11271:
11257:
11256:External links
11254:
11252:
11251:
11242:
11233:
11176:
11141:
11120:10.1.1.45.9310
11091:
11043:
10993:
10979:
10958:
10914:(6): 449â472.
10882:
10879:
10878:
10877:
10855:
10824:
10795:
10777:
10755:
10734:
10728:
10704:
10690:
10669:
10663:
10640:
10626:
10610:
10596:
10590:. OUP Oxford.
10584:Mosca, Michele
10575:
10561:
10548:
10534:
10513:
10491:
10465:
10459:
10438:
10416:
10395:
10381:
10368:
10346:
10325:
10311:
10288:
10285:
10284:
10282:
10279:
10278:
10277:
10271:
10239:Shor, Peter W.
10235:
10213:
10183:
10169:
10145:
10123:
10115:10.17226/25196
10102:
10088:
10062:
10059:
10057:
10056:
10015:
10013:, p. 201.
10003:
9991:
9989:, p. 126.
9979:
9967:
9965:, p. 126.
9955:
9953:, p. 119.
9943:
9941:, p. 114.
9931:
9929:, p. 127.
9919:
9882:(3): 1900052.
9862:
9848:
9828:
9802:
9781:
9755:
9736:
9715:
9677:hep-th/9406058
9670:(2): 992â997.
9654:
9635:
9620:
9555:
9508:
9471:(5): 544â552.
9451:
9382:
9356:
9330:
9279:
9253:
9222:
9161:
9112:
9037:
9022:
8986:
8943:
8922:
8896:
8870:
8851:
8814:(6): 595â600.
8808:Nature Physics
8798:
8747:
8726:
8705:
8662:Kitaev, Alexei
8649:
8588:
8529:
8504:
8471:
8450:
8377:
8328:
8285:
8232:
8181:
8158:
8105:
8084:
8062:
8000:
7979:
7926:
7891:Applied Energy
7877:
7824:
7773:
7728:(15): 150502.
7712:
7643:
7592:
7573:
7520:
7496:
7489:
7467:
7438:(1): 169â190.
7418:
7403:
7367:
7314:
7301:(1): 178â185.
7281:
7247:
7230:
7215:
7186:
7184:, p. 216.
7174:
7125:
7098:
7071:
7037:
6991:
6932:
6899:
6884:
6865:
6850:
6843:
6796:
6772:
6735:(3): 281â284.
6729:Nature Physics
6718:
6711:
6675:
6668:
6638:
6585:
6523:
6477:
6432:(3): 605â622.
6416:
6371:(4): 755â787.
6355:
6302:
6287:
6257:
6204:
6140:
6133:
6115:
6103:
6091:
6089:, p. 110.
6079:
6064:
6049:
6037:
6017:
5991:
5965:
5939:
5913:
5837:
5804:
5773:
5745:
5719:
5668:
5602:
5600:, p. 481.
5590:
5569:
5543:
5509:
5374:
5325:
5295:
5256:
5241:
5180:
5118:
5103:
5096:
5056:
5044:
5032:
5020:
5005:
4975:
4960:
4930:
4879:
4864:
4824:
4781:
4779:, p. 214.
4769:
4704:
4693:on 10 May 2013
4671:
4612:
4585:(5): 563â591.
4566:
4531:(6): 493â501.
4515:
4508:
4486:
4471:
4449:
4399:
4397:, p. 132.
4387:
4360:
4358:
4355:
4352:
4351:
4343:standard basis
4334:
4316:
4315:
4313:
4310:
4308:
4307:
4301:
4295:
4289:
4283:
4277:
4271:
4268:Quantum volume
4265:
4259:
4250:
4244:
4235:
4229:
4223:
4217:
4211:
4205:
4196:
4191:
4185:
4182:D-Wave Systems
4178:
4176:
4173:
4150:
4147:
4144:
4141:
4138:
4135:
4102:
4099:
4096:
4093:
4090:
4087:
4084:
4081:
4078:
4075:
4072:
4069:
4018:
4015:
4012:
4009:
4006:
4003:
4000:
3976:
3973:
3970:
3967:
3964:
3961:
3958:
3913:Main article:
3910:
3907:
3887:Turing machine
3863:
3860:
3858:
3855:
3850:superconductor
3820:
3817:
3816:
3815:
3773:
3772:
3764:
3757:
3754:
3747:
3740:
3715:
3712:
3689:Boson sampling
3655:
3652:
3561:dephasing time
3548:
3537:
3534:
3499:
3498:
3495:
3492:
3485:
3482:
3466:
3463:
3442:
3439:
3435:drug discovery
3404:Main article:
3401:
3398:
3385:
3382:
3361:
3360:
3357:
3354:
3330:
3327:
3324:
3321:
3301:
3296:
3291:
3288:
3264:
3245:Main article:
3242:
3239:
3193:DiffieâHellman
3145:Main article:
3142:
3139:
3107:Main article:
3104:
3101:
3019:
3016:
2970:
2967:
2945:
2942:
2934:Turing machine
2925:
2922:
2909:
2906:
2889:
2886:
2869:
2866:
2841:
2838:
2813:
2791:
2787:
2783:
2778:
2774:
2762:unitary matrix
2727:
2724:
2709:
2706:
2697:
2694:
2670:
2667:
2663:
2642:
2639:
2635:
2618:{\textstyle X}
2614:
2594:
2591:
2587:
2583:
2580:
2577:
2573:
2569:
2566:
2546:
2543:
2539:
2535:
2532:
2529:
2525:
2521:
2518:
2498:
2495:
2491:
2487:
2484:
2481:
2477:
2473:
2470:
2450:
2447:
2443:
2439:
2436:
2433:
2429:
2425:
2422:
2402:
2397:
2391:
2388:
2386:
2383:
2381:
2378:
2376:
2373:
2372:
2369:
2366:
2364:
2361:
2359:
2356:
2354:
2351:
2350:
2347:
2344:
2342:
2339:
2337:
2334:
2332:
2329:
2328:
2325:
2322:
2320:
2317:
2315:
2312:
2310:
2307:
2306:
2304:
2299:
2296:
2272:
2267:
2261:
2258:
2257:
2254:
2251:
2250:
2247:
2244:
2243:
2240:
2237:
2236:
2234:
2229:
2226:
2223:
2219:
2214:
2209:
2203:
2200:
2199:
2196:
2193:
2192:
2189:
2186:
2185:
2182:
2179:
2178:
2176:
2171:
2168:
2165:
2161:
2156:
2151:
2145:
2142:
2141:
2138:
2135:
2134:
2131:
2128:
2127:
2124:
2121:
2120:
2118:
2113:
2110:
2107:
2103:
2098:
2093:
2087:
2084:
2083:
2080:
2077:
2076:
2073:
2070:
2069:
2066:
2063:
2062:
2060:
2055:
2052:
2049:
2045:
2032:
2031:
2019:
2016:
2012:
2008:
2005:
2002:
1998:
1994:
1974:
1971:
1967:
1963:
1960:
1957:
1953:
1949:
1922:
1917:
1911:
1908:
1906:
1903:
1902:
1899:
1896:
1894:
1891:
1890:
1888:
1883:
1880:
1858:quantum memory
1847:
1844:
1719:tensor product
1655:
1652:
1648:
1627:
1624:
1620:
1599:
1596:
1592:
1586:
1580:
1576:
1573:
1570:
1567:
1563:
1557:
1551:
1547:
1527:
1524:
1519:
1514:
1509:
1505:
1501:
1496:
1491:
1486:
1482:
1461:
1441:
1419:
1414:
1409:
1405:
1384:
1381:
1377:
1354:
1349:
1344:
1340:
1319:
1316:
1312:
1287:
1284:
1280:
1276:
1273:
1270:
1267:
1263:
1259:
1246:describes the
1240:standard basis
1230:
1208:
1188:
1157:
1137:
1113:
1110:
1106:
1085:
1082:
1078:
1057:
1054:
1050:
1046:
1043:
1040:
1037:
1033:
1029:
1009:
977:
974:
970:
958:linear algebra
954:Dirac notation
934:
931:
927:
906:
903:
899:
870:
867:
863:
842:
839:
835:
814:
811:
807:
786:
783:
779:
739:
736:
732:
711:
708:
704:
683:
680:
676:
672:
669:
666:
663:
659:
655:
652:
649:
646:
642:
622:
619:
594:quantum states
578:linear algebra
542:may depend on
520:semiconductors
498:
495:
378:DiffieâHellman
359:RSA encryption
188:
185:
132:, introducing
58:that exploits
26:
9:
6:
4:
3:
2:
14425:
14414:
14411:
14409:
14406:
14404:
14403:Open problems
14401:
14399:
14396:
14394:
14391:
14389:
14386:
14384:
14381:
14379:
14376:
14374:
14371:
14369:
14366:
14365:
14363:
14348:
14340:
14339:
14336:
14330:
14327:
14325:
14322:
14320:
14317:
14313:
14310:
14309:
14308:
14305:
14304:
14302:
14298:
14292:
14289:
14287:
14284:
14280:
14277:
14276:
14275:
14272:
14270:
14267:
14265:
14262:
14260:
14257:
14256:
14254:
14250:
14244:
14241:
14239:
14236:
14234:
14231:
14229:
14226:
14224:
14221:
14219:
14216:
14214:
14211:
14209:
14206:
14204:
14201:
14199:
14196:
14194:
14191:
14189:
14186:
14184:
14183:Quantum logic
14181:
14179:
14176:
14174:
14171:
14169:
14166:
14164:
14161:
14159:
14156:
14154:
14151:
14149:
14146:
14142:
14139:
14138:
14137:
14134:
14132:
14129:
14127:
14124:
14122:
14119:
14115:
14112:
14111:
14110:
14107:
14105:
14102:
14100:
14097:
14095:
14092:
14091:
14089:
14087:
14083:
14077:
14074:
14072:
14069:
14067:
14064:
14062:
14059:
14057:
14054:
14052:
14049:
14047:
14044:
14042:
14039:
14037:
14036:Quantum chaos
14034:
14032:
14029:
14027:
14024:
14023:
14021:
14019:
14015:
14009:
14006:
14004:
14003:SternâGerlach
14001:
13999:
13996:
13994:
13991:
13989:
13986:
13984:
13981:
13979:
13976:
13974:
13971:
13969:
13966:
13964:
13961:
13959:
13956:
13955:
13953:
13949:
13943:
13940:
13938:
13937:Transactional
13935:
13933:
13930:
13928:
13927:Quantum logic
13925:
13923:
13920:
13918:
13915:
13909:
13906:
13905:
13904:
13901:
13900:
13899:
13896:
13894:
13891:
13889:
13886:
13884:
13881:
13879:
13876:
13874:
13871:
13870:
13868:
13866:
13862:
13856:
13853:
13851:
13848:
13846:
13843:
13841:
13838:
13836:
13833:
13832:
13830:
13826:
13820:
13817:
13815:
13812:
13810:
13807:
13805:
13802:
13800:
13797:
13795:
13792:
13790:
13787:
13786:
13784:
13780:
13772:
13769:
13767:
13764:
13763:
13762:
13761:Wave function
13759:
13757:
13754:
13752:
13749:
13747:
13744:
13742:
13739:
13737:
13736:Superposition
13734:
13732:
13731:Quantum state
13729:
13727:
13724:
13722:
13719:
13717:
13714:
13712:
13709:
13707:
13704:
13702:
13699:
13695:
13692:
13690:
13687:
13685:
13684:Excited state
13682:
13680:
13677:
13676:
13675:
13672:
13670:
13667:
13665:
13662:
13660:
13657:
13655:
13652:
13651:
13649:
13645:
13639:
13636:
13634:
13631:
13629:
13626:
13622:
13619:
13618:
13617:
13614:
13612:
13609:
13608:
13606:
13602:
13598:
13591:
13586:
13584:
13579:
13577:
13572:
13571:
13568:
13556:
13548:
13546:
13538:
13536:
13528:
13527:
13524:
13518:
13515:
13513:
13510:
13508:
13505:
13503:
13500:
13498:
13495:
13493:
13490:
13488:
13485:
13483:
13480:
13478:
13475:
13473:
13470:
13468:
13465:
13463:
13460:
13458:
13455:
13453:
13450:
13448:
13445:
13443:
13440:
13438:
13435:
13433:
13430:
13428:
13425:
13423:
13420:
13419:
13417:
13413:
13407:
13404:
13402:
13399:
13397:
13394:
13392:
13391:Mixed reality
13389:
13387:
13384:
13382:
13379:
13377:
13374:
13372:
13369:
13368:
13366:
13364:
13360:
13354:
13351:
13349:
13346:
13344:
13341:
13339:
13336:
13334:
13331:
13330:
13328:
13326:
13322:
13316:
13313:
13311:
13308:
13306:
13303:
13301:
13298:
13296:
13293:
13291:
13288:
13286:
13283:
13281:
13278:
13277:
13275:
13273:
13269:
13263:
13260:
13258:
13255:
13253:
13250:
13248:
13245:
13243:
13240:
13239:
13237:
13235:
13231:
13225:
13224:Accessibility
13222:
13220:
13219:Visualization
13217:
13215:
13212:
13210:
13207:
13205:
13202:
13201:
13199:
13197:
13193:
13187:
13184:
13182:
13179:
13177:
13174:
13172:
13169:
13167:
13164:
13162:
13159:
13157:
13154:
13152:
13149:
13147:
13144:
13143:
13141:
13139:
13135:
13129:
13126:
13124:
13121:
13119:
13116:
13114:
13111:
13109:
13106:
13104:
13101:
13099:
13096:
13094:
13091:
13089:
13086:
13084:
13081:
13079:
13076:
13074:
13071:
13069:
13066:
13064:
13061:
13060:
13058:
13056:
13052:
13046:
13043:
13041:
13038:
13036:
13033:
13031:
13028:
13026:
13023:
13021:
13018:
13016:
13013:
13011:
13008:
13007:
13005:
13003:
12998:
12992:
12989:
12987:
12984:
12982:
12979:
12977:
12974:
12972:
12969:
12968:
12966:
12964:
12960:
12954:
12951:
12949:
12946:
12944:
12941:
12939:
12936:
12934:
12931:
12929:
12926:
12924:
12921:
12920:
12918:
12916:
12912:
12906:
12903:
12901:
12898:
12896:
12893:
12891:
12888:
12886:
12883:
12881:
12878:
12876:
12873:
12871:
12868:
12866:
12863:
12861:
12858:
12857:
12855:
12853:
12849:
12843:
12840:
12838:
12835:
12833:
12830:
12828:
12825:
12823:
12820:
12818:
12815:
12813:
12810:
12808:
12805:
12803:
12800:
12798:
12795:
12794:
12792:
12790:
12786:
12782:
12776:
12773:
12771:
12768:
12766:
12763:
12761:
12758:
12756:
12753:
12752:
12750:
12746:
12740:
12737:
12735:
12732:
12730:
12727:
12725:
12722:
12720:
12717:
12715:
12712:
12711:
12709:
12707:
12703:
12697:
12694:
12692:
12689:
12687:
12686:Dependability
12684:
12682:
12679:
12677:
12674:
12673:
12671:
12667:
12661:
12657:
12654:
12652:
12649:
12647:
12644:
12642:
12639:
12637:
12634:
12632:
12629:
12627:
12624:
12622:
12619:
12617:
12614:
12612:
12609:
12608:
12606:
12604:
12600:
12595:
12589:
12585:
12578:
12573:
12571:
12566:
12564:
12559:
12558:
12555:
12543:
12542:
12533:
12532:
12529:
12519:
12516:
12514:
12511:
12509:
12506:
12504:
12501:
12497:
12496:Plasma window
12494:
12493:
12492:
12489:
12487:
12484:
12482:
12479:
12477:
12474:
12472:
12469:
12468:
12466:
12462:
12456:
12455:teleportation
12453:
12451:
12448:
12446:
12443:
12441:
12438:
12436:
12433:
12431:
12428:
12426:
12423:
12421:
12418:
12416:
12413:
12411:
12408:
12406:
12403:
12401:
12398:
12396:
12393:
12391:
12388:
12386:
12383:
12381:
12378:
12376:
12373:
12371:
12368:
12366:
12363:
12361:
12358:
12356:
12353:
12349:
12346:
12345:
12344:
12341:
12339:
12336:
12334:
12331:
12329:
12326:
12324:
12321:
12319:
12316:
12314:
12311:
12309:
12306:
12304:
12301:
12300:
12298:
12296:
12292:
12289:
12285:
12281:
12274:
12269:
12267:
12262:
12260:
12255:
12254:
12251:
12239:
12231:
12229:
12221:
12220:
12217:
12211:
12208:
12206:
12203:
12201:
12198:
12196:
12193:
12191:
12187:
12184:
12182:
12178:
12174:
12171:
12170:
12168:
12166:
12160:
12150:
12147:
12145:
12142:
12140:
12137:
12135:
12132:
12131:
12129:
12127:
12123:
12117:
12114:
12112:
12109:
12107:
12106:Spin qubit QC
12104:
12102:
12099:
12098:
12096:
12093:
12089:
12083:
12080:
12078:
12075:
12074:
12072:
12070:
12066:
12060:
12057:
12055:
12052:
12050:
12047:
12045:
12042:
12041:
12039:
12037:
12033:
12030:
12024:
12018:
12015:
12011:
12010:
12006:
12004:
12001:
11999:
11996:
11994:
11991:
11989:
11986:
11984:
11981:
11979:
11976:
11974:
11971:
11970:
11968:
11967:
11965:
11963:
11957:
11951:
11948:
11946:
11943:
11939:
11936:
11935:
11934:
11931:
11927:
11924:
11923:
11922:
11919:
11915:
11914:cluster state
11912:
11911:
11910:
11907:
11905:
11902:
11900:
11897:
11896:
11894:
11892:
11886:
11878:
11874:
11870:
11868:
11864:
11860:
11859:
11858:
11855:
11851:
11848:
11847:
11846:
11843:
11841:
11838:
11836:
11833:
11832:
11830:
11824:
11818:
11815:
11813:
11810:
11808:
11805:
11803:
11800:
11798:
11795:
11794:
11792:
11790:
11784:
11778:
11775:
11773:
11770:
11768:
11765:
11763:
11760:
11758:
11755:
11753:
11750:
11748:
11745:
11743:
11740:
11738:
11735:
11733:
11730:
11728:
11725:
11723:
11722:DeutschâJozsa
11720:
11718:
11715:
11713:
11710:
11708:
11705:
11704:
11702:
11700:
11696:
11686:
11683:
11679:
11676:
11674:
11671:
11669:
11666:
11665:
11664:
11661:
11659:
11658:Quantum money
11656:
11654:
11651:
11649:
11646:
11645:
11643:
11641:
11637:
11631:
11628:
11624:
11621:
11620:
11619:
11616:
11612:
11609:
11608:
11607:
11604:
11602:
11599:
11597:
11594:
11592:
11589:
11585:
11582:
11580:
11577:
11576:
11575:
11572:
11571:
11569:
11567:communication
11563:
11557:
11554:
11552:
11549:
11547:
11544:
11542:
11539:
11537:
11534:
11532:
11529:
11527:
11524:
11522:
11519:
11517:
11514:
11512:
11509:
11507:
11504:
11502:
11499:
11497:
11494:
11492:
11489:
11487:
11484:
11482:
11479:
11478:
11476:
11472:
11464:
11461:
11460:
11459:
11456:
11452:
11449:
11448:
11447:
11444:
11442:
11439:
11437:
11434:
11432:
11429:
11425:
11422:
11421:
11420:
11417:
11415:
11412:
11410:
11407:
11406:
11404:
11400:
11396:
11389:
11384:
11382:
11377:
11375:
11370:
11369:
11366:
11360:
11356:
11354:
11351:
11349:
11346:
11344:
11343:David Deutsch
11340:
11337:
11335:
11331:
11328:
11327:
11323:
11322:
11319:
11315:
11312:
11308:
11304:
11303:
11298:
11294:
11291:
11287:
11284:
11281:
11276:
11272:
11269:
11264:
11260:
11259:
11248:
11243:
11239:
11234:
11230:
11226:
11222:
11218:
11214:
11210:
11206:
11202:
11197:
11192:
11189:(2): 021318.
11188:
11184:
11183:
11177:
11173:
11169:
11164:
11159:
11155:
11151:
11147:
11142:
11138:
11134:
11130:
11126:
11121:
11116:
11112:
11108:
11104:
11100:
11096:
11092:
11087:
11083:
11079:
11075:
11070:
11065:
11061:
11057:
11053:
11049:
11044:
11040:
11036:
11032:
11028:
11024:
11020:
11015:
11010:
11006:
11002:
10998:
10994:
10990:
10986:
10982:
10976:
10972:
10968:
10964:
10959:
10955:
10951:
10947:
10946:2027.42/45526
10943:
10939:
10935:
10931:
10927:
10922:
10917:
10913:
10909:
10905:
10901:
10897:
10893:
10889:
10885:
10884:
10874:
10870:
10866:
10862:
10858:
10852:
10848:
10844:
10839:
10834:
10830:
10825:
10810:
10806:
10802:
10798:
10792:
10785:
10784:
10778:
10774:
10770:
10766:
10762:
10758:
10752:
10748:
10747:10.1142/11938
10744:
10740:
10735:
10731:
10725:
10721:
10717:
10713:
10709:
10705:
10701:
10697:
10693:
10687:
10683:
10679:
10675:
10670:
10666:
10660:
10656:
10652:
10648:
10647:
10641:
10637:
10633:
10629:
10623:
10619:
10615:
10611:
10607:
10603:
10599:
10593:
10589:
10585:
10581:
10576:
10572:
10568:
10564:
10558:
10554:
10549:
10545:
10541:
10537:
10531:
10527:
10523:
10519:
10514:
10510:
10506:
10502:
10498:
10494:
10488:
10484:
10480:
10473:
10472:
10466:
10462:
10456:
10452:
10448:
10444:
10439:
10435:
10431:
10427:
10423:
10419:
10413:
10409:
10405:
10401:
10396:
10392:
10388:
10384:
10378:
10375:. MIT Press.
10374:
10369:
10365:
10361:
10357:
10353:
10349:
10343:
10339:
10338:10.1142/10909
10335:
10331:
10326:
10322:
10318:
10314:
10308:
10304:
10300:
10296:
10291:
10290:
10274:
10268:
10264:
10260:
10256:
10252:
10248:
10244:
10240:
10236:
10232:
10228:
10224:
10220:
10216:
10210:
10206:
10202:
10198:
10197:
10192:
10191:Chuang, Isaac
10188:
10184:
10180:
10176:
10172:
10166:
10162:
10158:
10154:
10150:
10146:
10142:
10138:
10134:
10130:
10126:
10120:
10116:
10112:
10108:
10103:
10099:
10095:
10091:
10085:
10081:
10077:
10073:
10069:
10065:
10064:
10052:
10048:
10043:
10038:
10034:
10030:
10026:
10019:
10012:
10007:
10001:, p. 41.
10000:
9995:
9988:
9983:
9977:, p. 29.
9976:
9971:
9964:
9959:
9952:
9947:
9940:
9935:
9928:
9923:
9915:
9911:
9907:
9903:
9899:
9895:
9890:
9885:
9881:
9877:
9873:
9866:
9851:
9849:9783030420185
9845:
9841:
9840:
9832:
9817:
9816:IEEE Spectrum
9813:
9806:
9797:
9792:
9785:
9778:(5): 508â516.
9777:
9773:
9766:
9759:
9751:
9747:
9740:
9731:
9726:
9719:
9711:
9707:
9703:
9699:
9695:
9691:
9687:
9683:
9678:
9673:
9669:
9665:
9658:
9650:
9646:
9639:
9631:
9624:
9616:
9612:
9608:
9604:
9600:
9596:
9592:
9588:
9583:
9578:
9575:(3): 030601.
9574:
9570:
9566:
9559:
9551:
9547:
9543:
9539:
9535:
9531:
9527:
9523:
9519:
9512:
9504:
9500:
9496:
9492:
9488:
9484:
9479:
9474:
9470:
9466:
9462:
9455:
9447:
9443:
9439:
9435:
9431:
9427:
9423:
9419:
9415:
9411:
9406:
9401:
9397:
9393:
9386:
9371:
9367:
9360:
9345:
9341:
9334:
9326:
9322:
9318:
9314:
9310:
9306:
9302:
9298:
9295:(7838): 380.
9294:
9290:
9283:
9267:
9263:
9257:
9249:
9245:
9241:
9237:
9233:
9226:
9218:
9214:
9210:
9206:
9202:
9198:
9194:
9190:
9185:
9180:
9177:(9): 090502.
9176:
9172:
9165:
9157:
9153:
9148:
9143:
9139:
9135:
9131:
9127:
9123:
9116:
9108:
9104:
9099:
9094:
9090:
9086:
9082:
9078:
9074:
9070:
9065:
9060:
9056:
9052:
9048:
9041:
9033:
9029:
9025:
9019:
9015:
9011:
9006:
9001:
8997:
8990:
8982:
8978:
8974:
8970:
8966:
8962:
8958:
8954:
8947:
8938:
8933:
8926:
8911:
8907:
8900:
8885:
8881:
8874:
8866:
8862:
8855:
8847:
8843:
8839:
8835:
8831:
8827:
8822:
8817:
8813:
8809:
8802:
8793:
8788:
8784:
8780:
8775:
8770:
8766:
8762:
8758:
8751:
8742:
8737:
8730:
8722:
8721:
8720:New Scientist
8716:
8709:
8701:
8697:
8693:
8689:
8684:
8679:
8675:
8671:
8667:
8663:
8659:
8653:
8645:
8641:
8637:
8633:
8629:
8625:
8621:
8617:
8612:
8607:
8603:
8599:
8592:
8584:
8580:
8576:
8572:
8567:
8562:
8557:
8552:
8548:
8544:
8540:
8533:
8525:
8521:
8517:
8516:
8508:
8500:
8496:
8491:
8486:
8482:
8475:
8466:
8461:
8454:
8446:
8442:
8438:
8434:
8430:
8426:
8422:
8418:
8414:
8410:
8405:
8400:
8396:
8392:
8388:
8381:
8373:
8369:
8364:
8359:
8355:
8351:
8347:
8343:
8339:
8332:
8324:
8320:
8316:
8312:
8308:
8304:
8300:
8296:
8289:
8281:
8277:
8273:
8269:
8264:
8259:
8255:
8251:
8247:
8243:
8236:
8228:
8224:
8220:
8216:
8211:
8206:
8202:
8198:
8197:
8192:
8185:
8169:
8162:
8154:
8150:
8146:
8142:
8138:
8134:
8129:
8124:
8120:
8116:
8109:
8101:
8100:
8099:IEEE Spectrum
8095:
8088:
8080:
8073:
8071:
8069:
8067:
8058:
8054:
8050:
8046:
8041:
8036:
8032:
8028:
8024:
8020:
8016:
8009:
8007:
8005:
7995:
7990:
7983:
7975:
7971:
7967:
7963:
7959:
7955:
7950:
7945:
7942:(2): 021037.
7941:
7937:
7930:
7922:
7918:
7913:
7908:
7904:
7900:
7896:
7892:
7888:
7881:
7873:
7869:
7865:
7861:
7857:
7853:
7848:
7843:
7839:
7835:
7828:
7819:
7814:
7810:
7806:
7801:
7796:
7793:(2): 022308.
7792:
7788:
7784:
7777:
7769:
7765:
7761:
7757:
7753:
7749:
7745:
7741:
7736:
7731:
7727:
7723:
7716:
7708:
7704:
7700:
7696:
7692:
7688:
7684:
7680:
7676:
7672:
7667:
7662:
7658:
7654:
7647:
7639:
7635:
7630:
7625:
7620:
7615:
7611:
7607:
7603:
7596:
7588:
7584:
7577:
7569:
7565:
7561:
7557:
7553:
7549:
7544:
7539:
7535:
7531:
7524:
7515:
7510:
7506:
7500:
7492:
7486:
7482:
7478:
7471:
7463:
7459:
7455:
7451:
7446:
7441:
7437:
7433:
7429:
7422:
7414:
7410:
7406:
7400:
7396:
7392:
7387:
7382:
7378:
7371:
7363:
7359:
7355:
7351:
7347:
7343:
7338:
7333:
7329:
7325:
7318:
7309:
7304:
7300:
7296:
7292:
7285:
7277:
7273:
7269:
7265:
7258:
7251:
7244:
7240:
7234:
7226:
7222:
7218:
7212:
7208:
7204:
7200:
7193:
7191:
7183:
7178:
7167:
7163:
7159:
7155:
7151:
7147:
7143:
7136:
7129:
7113:
7109:
7102:
7086:
7082:
7075:
7060:
7056:
7052:
7048:
7041:
7033:
7027:
7026:cite AV media
7011:
7007:
7006:
7001:
6995:
6987:
6983:
6978:
6973:
6969:
6965:
6961:
6957:
6953:
6949:
6948:
6943:
6936:
6920:
6916:
6915:
6910:
6903:
6895:
6888:
6880:
6876:
6869:
6863:, p. 42.
6862:
6857:
6855:
6846:
6840:
6836:
6832:
6827:
6822:
6818:
6814:
6810:
6806:
6800:
6792:
6788:
6781:
6779:
6777:
6768:
6764:
6760:
6756:
6752:
6748:
6743:
6738:
6734:
6730:
6722:
6714:
6708:
6704:
6700:
6695:
6690:
6686:
6679:
6671:
6665:
6661:
6657:
6654:. p. 3.
6653:
6649:
6642:
6634:
6630:
6626:
6622:
6618:
6614:
6609:
6604:
6600:
6596:
6589:
6581:
6577:
6573:
6569:
6565:
6561:
6557:
6553:
6548:
6543:
6539:
6535:
6527:
6519:
6515:
6511:
6507:
6502:
6497:
6493:
6489:
6481:
6473:
6469:
6465:
6461:
6457:
6453:
6449:
6445:
6440:
6435:
6431:
6427:
6420:
6412:
6408:
6404:
6400:
6396:
6392:
6388:
6384:
6379:
6374:
6370:
6366:
6359:
6351:
6347:
6343:
6339:
6335:
6331:
6326:
6321:
6318:(2): 022312.
6317:
6313:
6306:
6298:
6294:
6290:
6288:0-8186-4370-6
6284:
6280:
6276:
6272:
6268:
6261:
6253:
6249:
6245:
6241:
6237:
6233:
6228:
6223:
6219:
6215:
6208:
6200:
6196:
6192:
6188:
6183:
6178:
6174:
6170:
6165:
6160:
6156:
6153:
6152:
6144:
6136:
6130:
6126:
6119:
6112:
6107:
6100:
6095:
6088:
6087:Aaronson 2013
6083:
6077:, p. 18.
6076:
6071:
6069:
6062:, p. 17.
6061:
6056:
6054:
6047:, p. 13.
6046:
6041:
6033:
6032:
6027:
6021:
6006:
6002:
5995:
5980:
5976:
5969:
5953:
5949:
5943:
5928:
5924:
5917:
5909:
5905:
5901:
5897:
5892:
5887:
5883:
5879:
5875:
5871:
5866:
5861:
5857:
5853:
5849:
5841:
5825:
5821:
5820:
5815:
5808:
5793:
5792:
5784:
5777:
5762:
5761:
5756:
5749:
5734:
5730:
5723:
5715:
5711:
5707:
5703:
5699:
5695:
5691:
5687:
5683:
5679:
5672:
5664:
5660:
5655:
5650:
5646:
5642:
5637:
5632:
5628:
5624:
5620:
5613:
5611:
5609:
5607:
5599:
5594:
5585:
5580:
5573:
5558:
5554:
5547:
5532:
5528:
5524:
5520:
5513:
5505:
5501:
5497:
5493:
5489:
5485:
5481:
5477:
5472:
5467:
5463:
5459:
5443:
5439:
5435:
5431:
5427:
5423:
5419:
5415:
5410:
5405:
5401:
5397:
5393:
5389:
5384:Lay summary:
5381:
5379:
5370:
5366:
5361:
5356:
5352:
5348:
5344:
5340:
5336:
5329:
5314:
5310:
5306:
5299:
5291:
5287:
5283:
5279:
5276:: 3408â3411.
5275:
5271:
5267:
5260:
5253:
5248:
5246:
5237:
5233:
5229:
5225:
5221:
5217:
5213:
5209:
5204:
5199:
5195:
5191:
5184:
5176:
5172:
5168:
5164:
5160:
5156:
5152:
5148:
5144:
5140:
5136:
5132:
5125:
5123:
5115:
5110:
5108:
5099:
5093:
5089:
5085:
5080:
5075:
5071:
5067:
5060:
5054:, p. 15.
5053:
5048:
5041:
5036:
5029:
5024:
5016:
5012:
5008:
5002:
4998:
4994:
4990:
4986:
4979:
4971:
4967:
4963:
4957:
4953:
4949:
4945:
4941:
4934:
4926:
4922:
4918:
4914:
4910:
4906:
4902:
4898:
4894:
4890:
4883:
4875:
4871:
4867:
4861:
4857:
4853:
4848:
4843:
4839:
4835:
4828:
4820:
4816:
4811:
4806:
4802:
4798:
4794:
4788:
4786:
4778:
4773:
4754:
4750:
4746:
4742:
4738:
4734:
4730:
4726:
4722:
4715:
4708:
4692:
4688:
4684:
4683:
4675:
4667:
4663:
4659:
4655:
4651:
4647:
4643:
4639:
4635:
4631:
4627:
4623:
4616:
4608:
4604:
4600:
4596:
4592:
4588:
4584:
4580:
4573:
4571:
4562:
4558:
4554:
4550:
4546:
4542:
4538:
4534:
4530:
4526:
4519:
4511:
4509:9780691164724
4505:
4501:
4497:
4490:
4482:
4478:
4474:
4468:
4464:
4460:
4453:
4445:
4441:
4437:
4433:
4429:
4425:
4421:
4417:
4410:
4403:
4396:
4395:Aaronson 2013
4391:
4376:
4372:
4365:
4361:
4348:
4344:
4338:
4331:
4327:
4321:
4317:
4305:
4304:Valleytronics
4302:
4299:
4296:
4293:
4290:
4287:
4286:Supercomputer
4284:
4281:
4278:
4275:
4272:
4269:
4266:
4263:
4260:
4254:
4251:
4248:
4245:
4239:
4236:
4233:
4232:Metacomputing
4230:
4227:
4224:
4221:
4218:
4215:
4212:
4209:
4206:
4200:
4197:
4195:
4192:
4189:
4186:
4183:
4180:
4179:
4172:
4170:
4166:
4139:
4122:
4118:
4082:
4070:
4057:
4053:
4049:
4040:
4036:
4034:
4007:
3965:
3946:
3942:
3938:
3934:
3930:
3927:The class of
3925:
3923:
3916:
3906:
3904:
3900:
3896:
3892:
3891:computability
3888:
3882:
3880:
3875:
3869:
3862:Computability
3854:
3851:
3846:
3843:
3838:
3836:
3832:
3826:
3813:
3809:
3808:
3807:
3805:
3801:
3797:
3793:
3789:
3785:
3782:
3779:
3770:
3765:
3762:
3758:
3755:
3751:
3748:
3745:
3741:
3739:accelerators.
3738:
3734:
3733:
3732:
3729:
3726:
3721:
3711:
3708:
3703:
3700:
3698:
3694:
3690:
3686:
3681:
3679:
3675:
3670:
3667:
3666:
3661:
3660:John Preskill
3651:
3649:
3645:
3641:
3637:
3632:
3620:
3616:
3612:
3608:
3604:
3598:
3595:
3591:
3586:
3584:
3583:pulse shaping
3579:
3576:
3574:
3570:
3566:
3562:
3558:
3554:
3547:
3543:
3533:
3531:
3526:
3524:
3520:
3516:
3512:
3508:
3504:
3496:
3493:
3490:
3486:
3483:
3480:
3479:
3478:
3476:
3472:
3462:
3456:
3452:
3447:
3438:
3436:
3431:
3429:
3425:
3421:
3420:HHL Algorithm
3416:
3414:
3407:
3397:
3395:
3390:
3381:
3379:
3375:
3371:
3367:
3358:
3355:
3352:
3351:
3350:
3347:
3345:
3325:
3294:
3286:
3278:
3262:
3254:
3248:
3238:
3236:
3235:
3229:
3225:
3222:
3218:
3214:
3213:coding theory
3210:
3206:
3201:
3198:
3194:
3190:
3186:
3182:
3178:
3174:
3173:cryptographic
3170:
3166:
3165:prime numbers
3162:
3158:
3154:
3148:
3138:
3135:
3134:Haber process
3131:
3127:
3122:
3120:
3116:
3110:
3100:
3098:
3094:
3089:
3087:
3083:
3079:
3075:
3070:
3068:
3064:
3060:
3056:
3052:
3048:
3044:
3040:
3036:
3031:
3029:
3025:
3015:
3013:
3009:
3004:
2999:
2997:
2993:
2989:
2985:
2981:
2976:
2969:Communication
2966:
2962:
2958:
2950:
2941:
2939:
2935:
2931:
2921:
2919:
2915:
2905:
2903:
2899:
2895:
2885:
2883:
2879:
2875:
2865:
2863:
2859:
2858:cluster state
2855:
2854:quantum gates
2851:
2847:
2837:
2835:
2831:
2827:
2811:
2789:
2785:
2781:
2776:
2772:
2763:
2758:
2756:
2752:
2751:quantum gates
2748:
2741:
2737:
2732:
2723:
2721:
2715:
2705:
2702:
2693:
2691:
2687:
2682:
2665:
2637:
2612:
2589:
2581:
2575:
2567:
2564:
2541:
2533:
2527:
2519:
2516:
2493:
2485:
2479:
2471:
2468:
2445:
2437:
2431:
2423:
2420:
2400:
2395:
2389:
2384:
2379:
2374:
2367:
2362:
2357:
2352:
2345:
2340:
2335:
2330:
2323:
2318:
2313:
2308:
2302:
2297:
2294:
2286:
2270:
2265:
2259:
2252:
2245:
2238:
2232:
2227:
2221:
2212:
2207:
2201:
2194:
2187:
2180:
2174:
2169:
2163:
2154:
2149:
2143:
2136:
2129:
2122:
2116:
2111:
2105:
2096:
2091:
2085:
2078:
2071:
2064:
2058:
2053:
2047:
2014:
2006:
2000:
1992:
1969:
1961:
1955:
1947:
1940:
1939:
1938:
1936:
1920:
1915:
1909:
1904:
1897:
1892:
1886:
1881:
1878:
1871:
1867:
1863:
1859:
1853:
1843:
1841:
1837:
1833:
1832:
1788:
1768:
1721:of the qubit
1720:
1676:
1672:
1667:
1650:
1622:
1594:
1584:
1578:
1574:
1571:
1565:
1555:
1549:
1545:
1525:
1522:
1517:
1507:
1499:
1494:
1484:
1459:
1439:
1417:
1407:
1379:
1352:
1342:
1314:
1301:
1282:
1274:
1271:
1265:
1257:
1249:
1245:
1241:
1237:
1232:
1228:
1226:
1222:
1206:
1186:
1178:
1174:
1172:
1155:
1135:
1127:
1108:
1080:
1052:
1044:
1041:
1035:
1027:
1007:
995:
972:
959:
955:
951:
946:
929:
901:
888:
887:superposition
884:
865:
837:
809:
781:
767:
763:
759:
758:
734:
706:
678:
670:
667:
661:
653:
650:
644:
631:
627:
617:
612:
610:
607:As physicist
605:
603:
599:
595:
591:
587:
583:
579:
575:
571:
567:
563:
561:
557:
553:
552:superposition
549:
545:
541:
537:
533:
529:
525:
521:
517:
513:
509:
504:
494:
492:
488:
484:
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402:
398:
393:
391:
387:
383:
379:
375:
371:
367:
360:
356:
352:
348:
346:
342:
341:superposition
338:
334:
331:in 1993, and
330:
327:in 1985, the
326:
322:
318:
314:
312:
308:
304:
300:
296:
292:
288:
284:
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237:
233:
229:
225:
221:
213:
209:
205:
200:
194:
184:
182:
181:
175:
171:
170:computability
167:
162:
160:
156:
152:
148:
144:
140:
135:
131:
127:
122:
120:
116:
112:
108:
104:
103:superposition
100:
96:
92:
88:
83:
81:
77:
73:
72:exponentially
69:
65:
61:
57:
53:
46:
42:
38:
34:
30:
19:
14135:
14066:Quantum mind
13978:FranckâHertz
13840:KleinâGordon
13789:Formulations
13782:Formulations
13711:Interference
13701:Entanglement
13679:Ground state
13674:Energy level
13647:Fundamentals
13611:Introduction
13487:Cyberwarfare
13146:Cryptography
12539:
12476:Anti-gravity
12420:metamaterial
12348:post-quantum
12343:cryptography
12337:
12134:Charge qubit
12059:KLM protocol
12008:
11872:
11862:
11556:Purification
11486:EastinâKnill
11418:
11300:
11186:
11180:
11156:(1): 52â59.
11153:
11149:
11102:
11098:
11051:
11047:
11004:
11000:
10962:
10911:
10907:
10888:Abbot, Derek
10828:
10816:. Retrieved
10809:the original
10782:
10738:
10711:
10673:
10649:. Springer.
10645:
10617:
10587:
10552:
10517:
10470:
10442:
10399:
10372:
10329:
10297:. Springer.
10294:
10242:
10194:
10152:
10106:
10071:
10032:
10028:
10018:
10006:
9994:
9982:
9970:
9958:
9946:
9934:
9922:
9879:
9875:
9865:
9853:. Retrieved
9842:. Springer.
9838:
9831:
9819:. Retrieved
9815:
9805:
9784:
9775:
9771:
9758:
9749:
9739:
9718:
9667:
9663:
9657:
9648:
9638:
9623:
9572:
9568:
9558:
9525:
9521:
9511:
9468:
9464:
9454:
9395:
9391:
9385:
9373:. Retrieved
9370:Science News
9369:
9359:
9347:. Retrieved
9343:
9333:
9292:
9288:
9282:
9270:. Retrieved
9265:
9256:
9239:
9235:
9225:
9174:
9170:
9164:
9129:
9125:
9115:
9054:
9050:
9040:
8995:
8989:
8956:
8946:
8925:
8913:. Retrieved
8909:
8899:
8887:. Retrieved
8883:
8873:
8864:
8854:
8811:
8807:
8801:
8764:
8760:
8750:
8729:
8718:
8708:
8676:(1): 31â38.
8673:
8669:
8652:
8601:
8597:
8591:
8546:
8542:
8532:
8514:
8507:
8480:
8474:
8453:
8394:
8390:
8380:
8345:
8341:
8331:
8298:
8294:
8288:
8245:
8241:
8235:
8203:(4): 64â70.
8200:
8194:
8184:
8172:. Retrieved
8161:
8118:
8114:
8108:
8097:
8087:
8022:
8018:
7982:
7939:
7935:
7929:
7894:
7890:
7880:
7837:
7833:
7827:
7790:
7786:
7776:
7725:
7721:
7715:
7656:
7652:
7646:
7609:
7605:
7595:
7586:
7576:
7536:(2): 22â35.
7533:
7529:
7523:
7499:
7476:
7470:
7435:
7431:
7421:
7376:
7370:
7327:
7323:
7317:
7298:
7294:
7284:
7267:
7263:
7250:
7239:pqcrypto.org
7233:
7198:
7177:
7166:the original
7145:
7141:
7128:
7116:. Retrieved
7111:
7101:
7089:. Retrieved
7084:
7074:
7062:. Retrieved
7050:
7040:
7014:. Retrieved
7004:
6994:
6951:
6945:
6935:
6923:. Retrieved
6912:
6902:
6887:
6878:
6868:
6808:
6799:
6732:
6728:
6721:
6684:
6678:
6647:
6641:
6598:
6594:
6588:
6537:
6533:
6526:
6491:
6487:
6480:
6429:
6425:
6419:
6368:
6364:
6358:
6315:
6311:
6305:
6270:
6260:
6217:
6213:
6207:
6154:
6149:
6143:
6124:
6118:
6106:
6094:
6082:
6040:
6030:
6020:
6008:. Retrieved
6004:
5994:
5982:. Retrieved
5978:
5968:
5956:. Retrieved
5951:
5942:
5930:. Retrieved
5926:
5916:
5855:
5851:
5840:
5828:. Retrieved
5817:
5807:
5795:. Retrieved
5789:
5776:
5764:. Retrieved
5758:
5748:
5736:. Retrieved
5732:
5722:
5681:
5677:
5671:
5626:
5622:
5593:
5572:
5560:. Retrieved
5556:
5546:
5536:25 September
5534:. Retrieved
5522:
5512:
5461:
5457:
5445:. Retrieved
5395:
5391:
5342:
5338:
5328:
5316:. Retrieved
5308:
5298:
5269:
5265:
5259:
5193:
5189:
5183:
5134:
5130:
5116:, p. 7.
5070:Philadelphia
5065:
5059:
5047:
5035:
5023:
4988:
4978:
4943:
4933:
4892:
4888:
4882:
4837:
4827:
4800:
4772:
4760:. Retrieved
4753:the original
4724:
4720:
4707:
4695:. Retrieved
4691:the original
4686:
4681:
4674:
4625:
4621:
4615:
4582:
4578:
4528:
4524:
4518:
4495:
4489:
4458:
4452:
4419:
4415:
4402:
4390:
4378:. Retrieved
4374:
4364:
4346:
4345:is also the
4337:
4320:
4045:
3926:
3918:
3883:
3871:
3847:
3842:trapped ions
3839:
3835:trapped ions
3828:
3811:
3786:
3783:
3774:
3744:entanglement
3730:
3717:
3706:
3704:
3701:
3682:
3671:
3663:
3657:
3648:braid theory
3633:
3618:
3614:
3610:
3606:
3602:
3599:
3587:
3580:
3577:
3560:
3545:
3539:
3527:
3500:
3468:
3459:
3432:
3417:
3409:
3387:
3369:
3368:, where the
3362:
3348:
3252:
3250:
3232:
3204:
3202:
3150:
3123:
3112:
3090:
3085:
3071:
3032:
3021:
3000:
2978:
2963:
2959:
2955:
2927:
2911:
2891:
2871:
2843:
2759:
2744:
2736:Toffoli gate
2717:
2700:
2699:
2683:
2033:
1855:
1839:
1829:
1767:vector space
1668:
1298:, the state
1248:norm-squared
1233:
1179:. If either
1169:
1126:basis states
1125:
947:
886:
883:vector space
881:belong to a
765:
755:
753:
630:Bloch sphere
614:
606:
564:
556:interference
506:
467:
463:
447:
443:
430:
424:
409:
401:trapped ions
394:
386:unstructured
364:
344:
315:
307:cryptography
289:, prompting
275:Paul Benioff
260:
254:used in the
244:World War II
217:
210:can exhibit
178:
168:rather than
163:
123:
84:
51:
49:
29:
14324:EPR paradox
14104:Quantum bus
13973:Double-slit
13951:Experiments
13917:Many-worlds
13855:Schrödinger
13819:Phase space
13809:Schrödinger
13799:Interaction
13756:Uncertainty
13726:Nonlocality
13721:Measurement
13716:Decoherence
13706:Hamiltonian
13497:Video games
13477:Digital art
13234:Concurrency
13103:Data mining
13015:Probability
12755:Interpreter
12491:Force field
12440:programming
12400:logic clock
12385:information
12360:electronics
12165:programming
12144:Phase qubit
12049:Circuit QED
11521:No-deleting
11463:cloud-based
10720:Basic Books
9528:(9): 9â15.
8915:16 November
7505:Grover, Lov
7270:: 114â116.
7243:Tanja Lange
7112:cen.acs.org
6540:(4): 1017.
6365:SIAM Review
6111:Mermin 2007
6075:Mermin 2007
6060:Mermin 2007
5402:: 505â510.
4762:28 February
4422:(9): 1365.
4253:Quantum bus
4169:NP-hardness
4165:NP-complete
3792:Paul Davies
3573:cosmic rays
3536:Decoherence
3489:decoherence
3473:has listed
3441:Engineering
3128:to produce
2882:Hamiltonian
2876:, based on
2726:Gate array
1675:state space
540:programmers
283:exponential
206:shows that
14362:Categories
14252:Extensions
14086:Technology
13932:Relational
13883:Copenhagen
13794:Heisenberg
13741:Tunnelling
13604:Background
13555:Glossaries
13427:E-commerce
13020:Statistics
12963:Algorithms
12760:Middleware
12616:Peripheral
12405:logic gate
12303:algorithms
12205:libquantum
12139:Flux qubit
12044:Cavity QED
11993:BaconâShor
11983:stabilizer
11511:No-cloning
11196:1904.06560
10865:1091358969
10838:1508.02595
10818:6 February
10805:1308951401
10765:1178715016
10571:1111634190
10501:1244536372
10426:1272953643
10391:1082867954
10356:1084428655
10133:1091904777
9889:1907.03505
9821:3 December
9796:2008.05177
9582:2212.04749
9405:2012.01625
9375:7 December
9349:7 December
9266:TechCrunch
9184:2111.03011
9064:2108.01622
9005:2110.14502
8937:1910.09534
8821:1608.00263
8774:1801.00862
8611:1905.09749
8556:1512.00796
8465:1603.09383
8404:2001.09190
8295:Cryogenics
8210:1912.01299
7994:2101.03438
7949:2101.08354
7897:: 117628.
7847:2003.00264
7840:: 107119.
7800:1510.07611
7666:1611.09347
7619:2005.12792
7016:4 February
6742:1905.09408
6694:1909.08396
6608:1903.09051
6547:1906.01645
6501:1906.01645
6010:9 February
6005:rcpmag.com
5932:9 December
5865:2312.03982
5830:8 December
5636:1801.00862
5584:2103.03074
5562:9 February
5471:1910.11333
5409:1910.11333
5318:4 December
5203:1812.09976
4810:2003.06557
4357:References
3909:Complexity
3812:No, never.
3788:Bill Unruh
3714:Skepticism
3658:Physicist
3465:Challenges
3396:problems.
3076:, and the
3041:, solving
3018:Algorithms
1850:See also:
1836:correlated
1787:Bell state
1472:such that
1229:amplitudes
960:, writing
501:See also:
390:Seth Lloyd
366:Peter Shor
355:Peter Shor
323:, such as
291:Yuri Manin
263:physicists
85:The basic
13958:Bell test
13828:Equations
13654:Born rule
13376:Rendering
13371:Animation
13002:computing
12953:Semantics
12651:Processor
12450:simulator
12338:computing
12308:amplifier
12111:NV center
11546:Threshold
11526:No-hiding
11491:Gleason's
11307:EMS Press
11229:119104251
11221:1931-9401
11172:236664155
11137:124545445
11115:CiteSeerX
11086:220110562
11064:CiteSeerX
10989:128255429
10873:118528258
10773:225498497
10700:212140089
10636:907358694
10544:186509710
10509:242566636
10434:238223274
10321:884786739
10287:Textbooks
10223:700706156
10179:422727925
10141:125635007
10098:829706638
10037:CiteSeerX
9914:195833616
9906:2511-9044
9607:0031-9007
9550:222349414
9542:1353-4858
9503:218831653
9487:0963-6625
9446:227254333
9430:0036-8075
9325:227282052
9217:251755796
9156:246910085
9089:2375-2548
9032:239036985
8981:211982610
8973:0036-8075
8741:1203.5813
8644:162183806
8636:2521-327X
8575:1550-4832
8524:923881411
8445:210920566
8429:1476-4687
8323:244005391
8315:0011-2275
8280:220110562
8258:CiteSeerX
8227:231715555
8057:258847001
7974:231662294
7921:0306-2619
7872:211678230
7864:0098-1354
7735:0811.3171
7691:0028-0836
7638:218889377
7454:1557-2862
7237:See also
7059:0017-8012
6826:1011.3245
6767:256703226
6759:1745-2473
6633:210942877
6580:174799187
6572:1943-8206
6464:0010-3616
6403:0036-1445
6297:195866146
6252:119628297
6227:0707.1889
6177:CiteSeerX
6164:0801.2193
5984:6 January
5958:5 January
5952:darpa.mil
5908:266052773
5882:1476-4687
5797:13 August
5714:203626236
5531:0362-4331
5504:204836822
5442:204836822
5400:Google AI
5236:119417908
5220:0009-2665
5159:0036-8075
5040:Shor 1994
4917:0080-4630
4749:124545445
4650:0036-8075
4607:122949592
4561:120294023
4553:0031-9120
4481:796812982
4444:216143449
4436:0011-3891
4380:9 January
4140:⊈
4083:⊆
4071:⊆
4008:⊊
3966:⊆
3897:like the
3800:Gil Kalai
3320:Ω
2992:adversary
2782:×
2669:⟩
2641:⟩
2593:⟩
2579:⟩
2568:
2545:⟩
2531:⟩
2520:
2497:⟩
2483:⟩
2472:
2449:⟩
2435:⟩
2424:
2225:⟩
2167:⟩
2109:⟩
2051:⟩
2018:⟩
2004:⟩
1973:⟩
1959:⟩
1831:entangled
1671:dimension
1654:⟩
1626:⟩
1598:⟩
1569:⟩
1508:β
1485:α
1460:β
1440:α
1408:β
1383:⟩
1343:α
1318:⟩
1300:collapses
1286:⟩
1275:β
1269:⟩
1258:α
1244:Born rule
1207:β
1187:α
1156:β
1136:α
1112:⟩
1084:⟩
1056:⟩
1045:β
1039:⟩
1028:α
1008:ψ
976:⟩
973:ψ
933:⟩
905:⟩
869:⟩
841:⟩
813:⟩
785:⟩
738:⟩
710:⟩
682:⟩
671:β
665:⟩
654:α
648:⟩
645:ψ
602:composing
536:decoheres
487:Princeton
412:Google AI
410:In 2019,
337:black box
151:ion traps
107:measuring
14347:Category
14141:Timeline
13893:Ensemble
13873:Bayesian
13766:Collapse
13638:Glossary
13621:Timeline
13535:Category
13363:Graphics
13138:Security
12807:Compiler
12706:Networks
12603:Hardware
12355:dynamics
12173:OpenQASM
12149:Transmon
12026:Physical
11826:Quantum
11727:Grover's
11501:Holevo's
11474:Theorems
11424:timeline
11414:NISQ era
11324:Lectures
11039:15439711
10954:34885835
10716:New York
10606:85896383
10586:(2007).
10364:62280636
10241:(1994).
10231:59717455
10193:(2010).
10151:(2007).
10070:(2013).
9710:13980886
9615:38307065
9495:32438851
9438:33273064
9317:33273711
9272:7 August
9209:36083655
9107:35080972
8483:: 4â18.
8437:32848227
8372:23783610
8153:15439711
8049:37225885
7760:19905613
7707:64536201
7699:28905917
7568:11326499
7481:Springer
7362:13403194
7225:61401925
7118:12 April
7091:12 April
7064:12 April
7010:Sibos TV
6986:37316724
6977:10266970
6919:Archived
6791:Archived
6199:14255125
5900:38056497
5891:10830422
5824:Archived
5819:Phys.org
5733:The Hill
5706:31578480
5663:44098998
5496:31645734
5447:27 April
5434:31645734
5398:(7779).
5369:31645740
5228:31469277
5175:43496899
4874:16118245
4666:17187000
4658:19797653
4175:See also
4119:and the
3929:problems
3697:Jiuzhang
3609:, where
3571:such as
3515:helium-3
3370:database
3234:Key size
3221:dihedral
3132:for the
3119:collider
3061:and the
2764:of size
1367:, or to
1236:measured
1168:are the
1068:, where
598:matrices
570:coherent
538:. While
534:quickly
528:isolated
126:isolated
56:computer
14300:Related
14279:History
14018:Science
13850:Rydberg
13616:History
13545:Outline
12445:sensing
12425:network
12410:machine
12380:imaging
12328:circuit
12323:channel
12295:Quantum
12163:Quantum
12101:Kane QC
11960:Quantum
11888:Quantum
11817:PostBQP
11787:Quantum
11772:Simon's
11565:Quantum
11402:General
11309:, 2001
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