39:
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antiferromagnetic interaction range. Britton, et al. from NIST has experimentally benchmarked Ising interactions in a system of hundreds of qubits for studies of quantum magnetism. Pagano, et al., reported a new cryogenic ion trapping system designed for long time storage of large ion chains demonstrating coherent one and two-qubit operations for chains of up to 44 ions. Joshi, et al., probed the quantum dynamics of 51 individually controlled ions, realizing a long-range interacting spin chain.
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218:(qubits). Previous endeavors were unable to go beyond 30 quantum bits. The capability of this simulator is 10 times more than previous devices. It has passed a series of important benchmarking tests that indicate a capability to solve problems in material science that are impossible to model on conventional computers.
242:
then caused the qubits to interact, mimicking the quantum behavior of materials otherwise very difficult to study in the laboratory. Although the two systems may outwardly appear dissimilar, their behavior is engineered to be mathematically identical. In this way, simulators allow researchers to vary
161:
is vastly complex. Conventional computers, including supercomputers, are inadequate for simulating quantum systems with as few as 30 particles because the dimension of the
Hilbert space grows exponentially with particle number. Better computational tools are needed to understand and rationally design
301:
Hamiltonian. Major aims of these experiments include identifying low-temperature phases or tracking out-of-equilibrium dynamics for various models, problems which are theoretically and numerically intractable. Other experiments have realized condensed matter models in regimes which are difficult or
166:
of hundreds of particles. Quantum simulators provide an alternative route to understanding the properties of these systems. These simulators create clean realizations of specific systems of interest, which allows precise realizations of their properties. Precise control over and broad tunability of
42:
Trapped ion quantum simulator illustration: The heart of the simulator is a two-dimensional crystal of beryllium ions (blue spheres in the graphic); the outermost electron of each ion is a quantum bit (qubit, red arrows). The ions are confined by a large magnetic field in a device called a
Penning
250:
Friedenauer et al., adiabatically manipulated 2 spins, showing their separation into ferromagnetic and antiferromagnetic states. Kim et al., extended the trapped ion quantum simulator to 3 spins, with global antiferromagnetic Ising interactions featuring frustration and showing the link between
260:
demonstrated digital quantum simulation with up to 6 ions. Islam, et al., demonstrated adiabatic quantum simulation of the transverse Ising model with variable (long) range interactions with up to 18 trapped ion spins, showing control of the level of spin frustration by adjusting the
1236:
Britton, Joseph W.; Sawyer, Brian C.; Keith, Adam C.; Wang, C.-C. Joseph; Freericks, James K.; Uys, Hermann; Biercuk, Michael J.; Bollinger, John J. (25 April 2012). "Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins".
1521:
Lanyon, B. P.; Hempel, C.; Nigg, D.; Muller, M.; Gerritsma, R.; Zahringer, F.; Schindler, P.; Barreiro, J. T.; Rambach, M.; Kirchmair, G.; Hennrich, M.; Zoller, P.; Blatt, R.; Roos, C. F. (1 September 2011). "Universal
Digital Quantum Simulation with Trapped Ions".
1459:
Barreiro, Julio T.; MĂĽller, Markus; Schindler, Philipp; Nigg, Daniel; Monz, Thomas; Chwalla, Michael; Hennrich, Markus; Roos, Christian F.; Zoller, Peter; Blatt, Rainer (23 February 2011). "An open-system quantum simulator with trapped ions".
255:
between paramagnetic and ferromagnetic ordering as the number of spins increased from 2 to 9. Barreiro et al. created a digital quantum simulator of interacting spins with up to 5 trapped ions by coupling to an open reservoir and Lanyon
1648:
Pagano, G; Hess, P W; Kaplan, H B; Tan, W L; Richerme, P; Becker, P; Kyprianidis, A; Zhang, J; Birckelbaw, E; Hernandez, M R; Wu, Y; Monroe, C (9 October 2018). "Cryogenic trapped-ion system for large scale quantum simulation".
170:
Quantum simulators can solve problems which are difficult to simulate on classical computers because they directly exploit quantum properties of real particles. In particular, they exploit a property of quantum mechanics called
1858:
Jotzu, Gregor; Messer, Michael; Desbuquois, RĂ©mi; Lebrat, Martin; Uehlinger, Thomas; Greif, Daniel; Esslinger, Tilman (13 November 2014). "Experimental realization of the topological
Haldane model with ultracold fermions".
237:
and is used as a qubit, the quantum equivalent of a “1” or a “0” in a conventional computer. In the benchmarking experiment, physicists used laser beams to cool the ions to near absolute zero. Carefully timed microwave and
1398:; Kim, K.; Korenblit, S.; Noh, C.; Carmichael, H.; Lin, G.-D.; Duan, L.-M.; Joseph Wang, C.-C.; Freericks, J.K.; Monroe, C. (5 July 2011). "Onset of a quantum phase transition with a trapped ion quantum simulator".
179:
is made to be in two distinct states at the same time, for example, aligned and anti-aligned with an external magnetic field. Crucially, simulators also take advantage of a second quantum property called
2239:
Fitzpatrick, Mattias; Sundaresan, Neereja M.; Li, Andy C. Y.; Koch, Jens; Houck, Andrew A. (10 February 2017). "Observation of a
Dissipative Phase Transition in a One-Dimensional Circuit QED Lattice".
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Ma, Ruichao; Saxberg, Brendan; Owens, Clai; Leung, Nelson; Lu, Yao; Simon, Jonathan; Schuster, David I. (6 February 2019). "A dissipatively stabilized Mott insulator of photons".
27:, indicating the qubits are all in the same state (either "1" or "0"). Under the right experimental conditions, the ion crystal spontaneously forms this nearly perfect triangular
111:
over classical computers in terms of computability, but it is suspected that they can solve certain problems faster than classical computers, meaning they may be in different
1082:
Semeghini, G.; Levine, H.; Keesling, A.; Ebadi, S.; Wang, T. T.; Bluvstein, D.; Verresen, R.; Pichler, H.; Kalinowski, M.; Samajdar, R.; Omran, A. (2021-12-03).
1587:; Wang, C.- C. J.; Freericks, J. K.; Monroe, C. (2 May 2013). "Emergence and Frustration of Magnetism with Variable-Range Interactions in a Quantum Simulator".
468:
Britton, Joseph W.; Sawyer, Brian C.; Keith, Adam C.; Wang, C.-C. Joseph; Freericks, James K.; Uys, Hermann; Biercuk, Michael J.; Bollinger, John J. (2012).
984:
Kyprianidis, A.; Machado, F.; Morong, W.; Becker, P.; Collins, K. S.; Else, D. V.; Feng, L.; Hess, P. W.; Nayak, C.; Pagano, G.; Yao, N. Y. (2021-06-11).
107:. The simulation of a quantum physics by a classical computer has been shown to be inefficient. In other words, quantum computers provide no additional
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2006:
Alberti, Andrea; Robens, Carsten; Alt, Wolfgang; Brakhane, Stefan; Karski, Michał; Reimann, René; Widera, Artur; Meschede, Dieter (2016-05-06).
443:
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Berry, Dominic W.; Graeme Ahokas; Richard Cleve; Sanders, Barry C. (2007). "Efficient quantum algorithms for simulating sparse
Hamiltonians".
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1343:; Freericks, J. K.; Lin, G.-D.; Duan, L.-M.; Monroe, C. (June 2010). "Quantum simulation of frustrated Ising spins with trapped ions".
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Zhang, Dan-Wei; Zhu, Yan-Qing; Zhao, Y. X.; Yan, Hui; Zhu, Shi-Liang (29 March 2019). "Topological quantum matter with cold atoms".
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Kliesch, M.; Barthel, T.; Gogolin, C.; Kastoryano, M.; Eisert, J. (12 September 2011). "Dissipative
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527:
Note: This manuscript is a contribution of the US National
Institute of Standards and Technology and is not subject to US copyright.
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in a programmable fashion. In this instance, simulators are special purpose devices designed to provide insight about specific
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similar to the number of particles in the original system. This has been extended to much larger classes of quantum systems.
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frustration and entanglement and Islam et al., used adiabatic quantum simulation to demonstrate the sharpening of a
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Bloch, Immanuel; Dalibard, Jean; Nascimbene, Sylvain (2012). "Quantum simulations with ultracold quantum gases".
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Joshi, M.K.; Kranzl, F.; Schuckert, A.; Lovas, I.; Maier, C.; Blatt, R.; Knap, M.; Roos, C.F. (13 May 2022).
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2307:
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Dorit
Aharonov; Amnon Ta-Shma (2003). "Adiabatic Quantum State Generation and Statistical Zero Knowledge".
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determine ground states of certain
Hamiltonians after an adiabatic ramp. This approach is sometimes called
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470:"Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins"
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293:. A common thread for these experiments is the capability of realizing generic Hamiltonians, such as the
192:
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Paraoanu, G. S. (4 April 2014). "Recent Progress in Quantum Simulation Using Superconducting Circuits".
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103:(and therefore any simpler quantum simulator), meaning they are equivalent from the point of view of
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Childs, Andrew M. (2010). "On the relationship between continuous- and discrete-time quantum walk".
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Quantum simulators have been realized on a number of experimental platforms, including systems of
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Monroe, C; et, al (2021). "Programmable quantum simulations of spin systems with trapped ions".
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Quantum simulators using superconducting qubits fall into two main categories. First, so called
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parameters of the system allows the influence of various parameters to be cleanly disentangled.
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141:, polar molecules, trapped ions, photonic systems, quantum dots, and superconducting circuits.
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and studies of phase transitions in lattices of superconducting resonators coupled to qubits.
326:. Second, many systems emulate specific Hamiltonians and study their ground state properties,
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Johnson, Tomi H.; Clark, Stephen R.; Jaksch, Dieter (2014). "What is a quantum simulator?".
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based system forms an ideal setting for simulating interactions in quantum spin models. A
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2067:"Quantum Walks with Neutral Atoms: Quantum Interference Effects of One and Two Particles"
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Friedenauer, A.; Schmitz, H.; Glueckert, J. T.; Porras, D.; Schaetz, T. (27 July 2008).
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problems. Quantum simulators may be contrasted with generally programmable "digital"
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experiments are examples of quantum simulators. These include experiments studying
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73:
1984:
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330:, or time dynamics. Several important recent results include the realization of a
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The trapped-ion simulator consists of a tiny, single-plane crystal of hundreds of
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119:, the idea that there are problems only quantum Turing machines can solve in any
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Robens, Carsten; Brakhane, Stefan; Meschede, Dieter; Alberti, A. (2016-09-18),
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of many particles could be simulated by a quantum computer using a number of
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24:
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Islam, R.; Senko, C.; Campbell, W. C.; Korenblit, S.; Smith, J.; Lee, A.;
912:
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718:
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225:, less than 1 millimeter in diameter, hovering inside a device called a
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3074:
2938:
1429:
653:
606:
77:
65:, which would be capable of solving a wider class of quantum problems.
1787:
1324:
1299:
1084:"Probing topological spin liquids on a programmable quantum simulator"
962:
703:
243:
parameters that couldn’t be changed in natural solids, such as atomic
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629:
222:
1938:
1921:
399:
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materials whose properties are believed to depend on the collective
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1975:
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NIST Physicists Benchmark Quantum Simulator with Hundreds of Qubits
230:
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203:
2139:
1873:
1601:
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1474:
1412:
1251:
1059:"Creating Time Crystals Using New Quantum Computing Architectures"
824:
771:
489:
390:
3135:
2752:
2008:"Super-resolution microscopy of single atoms in optical lattices"
1696:"Observing emergent hydrodynamics in a long-range quantum magnet"
1297:
58:
43:
trap (not shown). Inside the trap the crystal rotates clockwise.
3112:
2608:
809:
302:
impossible to realize with conventional materials, such as the
1811:"Quantum simulations with ultracold atoms in optical lattices"
983:
2381:
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547:] (in Russian). Sov.Radio. pp. 13–15. Archived from
131:
1081:
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2238:
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682:
211:
23:
In this photograph of a quantum simulator crystal the ions
2747:
2732:
1693:
1149:"Quantum Simulators Create a Totally New Phase of Matter"
2005:
1393:
214:
can engineer and control interactions among hundreds of
1809:
Gross, Christian; Bloch, Immanuel (September 8, 2017).
1765:
1520:
1338:
1235:
467:
187:
Recently quantum simulators have been used to obtain
2574:
2177:
1647:
986:"Observation of a prethermal discrete time crystal"
530:
883:Lloyd, S. (1996). "Universal quantum simulators".
375:
157:, remain poorly understood because the underlying
1339:Kim, K.; Chang, M.-S.; Korenblit, S.; Islam, R.;
3490:
864:
2329:
1960:
1300:"Simulating a quantum magnet with trapped ions"
936:"Goals and opportunities in quantum simulation"
149:Many important problems in physics, especially
1057:S, Robert; ers; Berkeley, U. C. (2021-11-10).
444:National Institute of Standards and Technology
87:A quantum system may be simulated by either a
3200:
2315:
1231:
1229:
575:(1982). "Simulating Physics with Computers".
536:
435:
210:simulator, built by a team that included the
1056:
634:International Journal of Theoretical Physics
577:International Journal of Theoretical Physics
264:
933:
871:Nature Physics Insight – Quantum Simulation
144:
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2308:
1808:
1226:
369:
3214:
2252:
2191:
2138:
2078:
2041:
2023:
1974:
1937:
1922:"Magnetic fields without magnetic fields"
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1834:
1711:
1662:
1600:
1535:
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1411:
1323:
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1185:
1165:
1099:
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934:Cirac, J. Ignacio; Zoller, Peter (2012).
882:
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463:
461:
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421:
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313:
198:
2124:
1171:
37:
18:
16:Simulators of quantum mechanical systems
2840:Continuous-variable quantum information
627:
571:
3491:
759:Communications in Mathematical Physics
756:
706:Communications in Mathematical Physics
456:
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2303:
1919:
927:
567:
565:
1920:Simon, Jonathan (13 November 2014).
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2073:, WORLD SCIENTIFIC, pp. 1–15,
630:"Simulating physics with computers"
13:
2127:Journal of Low Temperature Physics
628:Feynman, Richard P. (1982-06-01).
621:
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14:
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3159:
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430: This article incorporates
425:
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1999:
1954:
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1802:
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1687:
1641:
1576:
1514:
1452:
1387:
1332:
1291:
1140:
1075:
1050:
977:
803:
1651:Quantum Science and Technology
842:10.1103/PhysRevLett.107.120501
750:
697:
676:
1:
2835:Adiabatic quantum computation
2043:10.1088/1367-2630/18/5/053010
1985:10.1080/00018732.2019.1594094
905:10.1126/science.273.5278.1073
363:
2886:Topological quantum computer
1204:10.1103/RevModPhys.93.025001
1147:Wood, Charlie (2021-12-02).
545:Computable and Noncomputable
7:
3164:Quantum information science
2331:Quantum information science
540:Vychislimoe i nevychislimoe
341:
324:adiabatic quantum computing
233:of each ion acts as a tiny
70:universal quantum simulator
10:
3517:
3454:Thermoacoustic heat engine
2559:quantum gate teleportation
2089:10.1142/9789813200616_0001
101:universal quantum computer
3466:
3439:Immersive virtual reality
3399:
3229:
3222:
3154:
3097:
3060:
3026:
3003:
2970:
2961:
2894:
2823:
2761:
2721:
2688:Quantum Fourier transform
2633:
2584:Post-quantum cryptography
2527:Entanglement distillation
2500:
2409:
2337:
2271:10.1103/PhysRevX.7.011016
2210:10.1038/s41586-019-0897-9
2157:10.1007/s10909-014-1175-8
873:. Nature.com. April 2012.
789:10.1007/s00220-009-0930-1
736:10.1007/s00220-006-0150-x
328:quantum phase transitions
285:, the unitary Fermi gas,
265:Ultracold atom simulators
3422:Digital scent technology
3174:Quantum mechanics topics
2869:Quantum machine learning
2845:One-way quantum computer
2698:Quantum phase estimation
2599:Quantum key distribution
2532:Monogamy of entanglement
1673:10.1088/2058-9565/aae0fe
334:in a driven-dissipative
145:Solving physics problems
2781:Randomized benchmarking
2643:Amplitude amplification
1836:10.1126/science.aal3837
1730:10.1126/science.abk2400
1619:10.1126/science.1232296
1554:10.1126/science.1208001
1118:10.1126/science.abi8794
1020:10.1126/science.abg8102
812:Physical Review Letters
308:Harper-Hofstadter model
151:low-temperature physics
139:ultracold quantum gases
3444:Magnetic refrigeration
2881:Quantum Turing machine
2874:quantum neural network
2621:Quantum secret sharing
2012:New Journal of Physics
537:Manin, Yu. I. (1980).
432:public domain material
378:EPJ Quantum Technology
353:Quantum Turing machine
348:Hamiltonian simulation
314:Superconducting qubits
299:transverse-field Ising
199:Trapped-ion simulators
99:is able to simulate a
93:quantum Turing machine
53:permit the study of a
47:
35:
3417:Cloak of invisibility
3216:Emerging technologies
2953:Entanglement-assisted
2914:quantum convolutional
2589:Quantum coin flipping
2554:Quantum teleportation
2515:entanglement-assisted
2345:DiVincenzo's criteria
1400:Nature Communications
41:
22:
2764:processor benchmarks
2693:Quantum optimization
2576:Quantum cryptography
2387:physical vs. logical
2295:Deutsch's 1985 paper
193:quantum spin liquids
105:computability theory
45:Credit: Britton/NIST
33:Credit: Britton/NIST
3449:Phased-array optics
3407:Acoustic levitation
2477:Quantum speed limit
2372:Quantum programming
2367:Quantum information
2263:2017PhRvX...7a1016F
2202:2019Natur.566...51M
2149:2014JLTP..175..633P
2034:2016NJPh...18e3010A
1963:Advances in Physics
1891:10.1038/nature13915
1883:2014Natur.515..237J
1827:2017Sci...357..995G
1780:2012NatPh...8..267B
1722:2022Sci...376..720J
1611:2013Sci...340..583I
1546:2011Sci...334...57L
1492:10.1038/nature09801
1484:2011Natur.470..486B
1422:2011NatCo...2..377I
1365:10.1038/nature09071
1357:2010Natur.465..590K
1316:2008NatPh...4..757F
1269:10.1038/nature10981
1261:2012Natur.484..489B
1196:2021RvMP...93b5001M
1110:2021Sci...374.1242S
1094:(6572): 1242–1247.
1012:2021Sci...372.1192K
996:(6547): 1192–1196.
955:2012NatPh...8..264C
897:1996Sci...273.1073L
834:2011PhRvL.107l0501K
781:2010CMaPh.294..581C
728:2007CMaPh.270..359B
646:1982IJTP...21..467F
589:1982IJTP...21..467F
507:10.1038/nature10981
499:2012Natur.484..489B
436:Michael E. Newman.
336:Bose-Hubbard system
3126:Forest/Rigetti QCS
2862:quantum logic gate
2648:Bernstein–Vazirani
2635:Quantum algorithms
2510:Classical capacity
2394:Quantum processors
2377:Quantum simulation
2071:Laser Spectroscopy
1821:(6355): 995–1001.
1430:10.1038/ncomms1374
654:10.1007/BF02650179
607:10.1007/BF02650179
113:complexity classes
51:Quantum simulators
48:
36:
3499:Quantum computing
3486:
3485:
3462:
3461:
3269:complexity theory
3254:cellular automata
3182:
3181:
3093:
3092:
2990:Linear optical QC
2771:Quantum supremacy
2725:complexity theory
2678:Quantum annealing
2629:
2628:
2566:Superdense coding
2355:Quantum computing
2241:Physical Review X
2098:978-981-320-060-9
1932:(7526): 202–203.
1867:(7526): 237–240.
1788:10.1038/nphys2259
1595:(6132): 583–587.
1468:(7335): 486–491.
1351:(7298): 590–593.
1325:10.1038/nphys1032
1245:(7395): 489–492.
963:10.1038/nphys2275
358:Quantum computing
320:quantum annealers
159:quantum mechanics
155:many-body physics
117:quantum supremacy
95:, as a classical
63:quantum computers
3506:
3474:
3473:
3351:machine learning
3326:key distribution
3311:image processing
3301:error correction
3227:
3226:
3209:
3202:
3195:
3186:
3185:
3172:
3171:
3162:
3161:
2968:
2967:
2898:error correction
2827:computing models
2793:Relaxation times
2683:Quantum counting
2572:
2571:
2520:quantum capacity
2467:No-teleportation
2452:No-communication
2324:
2317:
2310:
2301:
2300:
2283:
2282:
2256:
2236:
2230:
2229:
2195:
2175:
2169:
2168:
2142:
2133:(5–6): 633–654.
2122:
2116:
2115:
2114:
2113:
2082:
2062:
2056:
2055:
2045:
2027:
2003:
1997:
1996:
1978:
1958:
1952:
1951:
1941:
1917:
1911:
1910:
1876:
1855:
1849:
1848:
1838:
1806:
1800:
1799:
1763:
1757:
1756:
1754:
1752:
1715:
1706:(376): 720–724.
1691:
1685:
1684:
1666:
1645:
1639:
1638:
1604:
1580:
1574:
1573:
1539:
1518:
1512:
1511:
1477:
1456:
1450:
1449:
1415:
1391:
1385:
1384:
1336:
1330:
1329:
1327:
1295:
1289:
1288:
1254:
1233:
1224:
1223:
1189:
1169:
1163:
1162:
1160:
1159:
1144:
1138:
1137:
1103:
1079:
1073:
1072:
1070:
1069:
1054:
1048:
1047:
1005:
981:
975:
974:
940:
931:
925:
924:
891:(5278): 1073–8.
880:
874:
868:
862:
861:
827:
807:
801:
800:
774:
754:
748:
747:
721:
719:quant-ph/0508139
701:
695:
694:
692:
690:quant-ph/0301023
680:
674:
673:
625:
619:
618:
600:
583:(6–7): 467–488.
573:Feynman, Richard
569:
560:
559:
557:
556:
534:
528:
526:
492:
483:(7395): 489–92.
474:
465:
454:
453:
451:
450:
429:
428:
423:
412:
411:
393:
373:
291:optical tweezers
283:optical lattices
253:phase transition
229:. The outermost
177:quantum particle
164:quantum behavior
123:amount of time.
74:quantum computer
3516:
3515:
3509:
3508:
3507:
3505:
3504:
3503:
3489:
3488:
3487:
3482:
3458:
3395:
3306:finite automata
3218:
3213:
3183:
3178:
3150:
3100:
3089:
3062:Superconducting
3056:
3022:
3013:Neutral atom QC
3005:Ultracold atoms
2999:
2964:implementations
2963:
2957:
2897:
2890:
2857:Quantum circuit
2825:
2819:
2813:
2803:
2763:
2757:
2724:
2717:
2673:Hidden subgroup
2625:
2614:other protocols
2570:
2547:quantum network
2542:Quantum channel
2502:
2496:
2442:No-broadcasting
2432:Gottesman–Knill
2405:
2333:
2328:
2291:
2286:
2237:
2233:
2186:(7742): 51–57.
2176:
2172:
2123:
2119:
2111:
2109:
2099:
2063:
2059:
2004:
2000:
1959:
1955:
1939:10.1038/515202a
1918:
1914:
1856:
1852:
1807:
1803:
1764:
1760:
1750:
1748:
1692:
1688:
1646:
1642:
1581:
1577:
1530:(6052): 57–61.
1519:
1515:
1457:
1453:
1392:
1388:
1337:
1333:
1310:(10): 757–761.
1296:
1292:
1234:
1227:
1170:
1166:
1157:
1155:
1153:Quanta Magazine
1145:
1141:
1080:
1076:
1067:
1065:
1055:
1051:
982:
978:
938:
932:
928:
881:
877:
869:
865:
808:
804:
755:
751:
702:
698:
681:
677:
626:
622:
570:
563:
554:
552:
535:
531:
472:
466:
457:
448:
446:
426:
424:
415:
400:10.1140/epjqt10
374:
370:
366:
344:
316:
267:
245:lattice spacing
201:
147:
82:Richard Feynman
25:are fluorescing
17:
12:
11:
5:
3514:
3513:
3502:
3501:
3484:
3483:
3481:
3480:
3467:
3464:
3463:
3460:
3459:
3457:
3456:
3451:
3446:
3441:
3436:
3435:
3434:
3424:
3419:
3414:
3409:
3403:
3401:
3397:
3396:
3394:
3393:
3388:
3383:
3378:
3373:
3368:
3366:neural network
3363:
3358:
3353:
3348:
3343:
3338:
3333:
3328:
3323:
3318:
3313:
3308:
3303:
3298:
3293:
3288:
3287:
3286:
3276:
3271:
3266:
3261:
3256:
3251:
3246:
3241:
3235:
3233:
3224:
3220:
3219:
3212:
3211:
3204:
3197:
3189:
3180:
3179:
3177:
3176:
3166:
3155:
3152:
3151:
3149:
3148:
3146:many others...
3143:
3138:
3133:
3128:
3119:
3105:
3103:
3095:
3094:
3091:
3090:
3088:
3087:
3082:
3077:
3072:
3066:
3064:
3058:
3057:
3055:
3054:
3049:
3044:
3039:
3033:
3031:
3024:
3023:
3021:
3020:
3018:Trapped-ion QC
3015:
3009:
3007:
3001:
3000:
2998:
2997:
2992:
2987:
2982:
2976:
2974:
2972:Quantum optics
2965:
2959:
2958:
2956:
2955:
2950:
2949:
2948:
2941:
2936:
2931:
2926:
2921:
2916:
2911:
2902:
2900:
2892:
2891:
2889:
2888:
2883:
2878:
2877:
2876:
2866:
2865:
2864:
2854:
2853:
2852:
2842:
2837:
2831:
2829:
2821:
2820:
2818:
2817:
2816:
2815:
2811:
2805:
2801:
2790:
2789:
2788:
2778:
2776:Quantum volume
2773:
2767:
2765:
2759:
2758:
2756:
2755:
2750:
2745:
2740:
2735:
2729:
2727:
2719:
2718:
2716:
2715:
2710:
2705:
2700:
2695:
2690:
2685:
2680:
2675:
2670:
2665:
2660:
2655:
2653:Boson sampling
2650:
2645:
2639:
2637:
2631:
2630:
2627:
2626:
2624:
2623:
2618:
2617:
2616:
2611:
2606:
2596:
2591:
2586:
2580:
2578:
2569:
2568:
2563:
2562:
2561:
2551:
2550:
2549:
2539:
2534:
2529:
2524:
2523:
2522:
2517:
2506:
2504:
2498:
2497:
2495:
2494:
2489:
2487:Solovay–Kitaev
2484:
2479:
2474:
2469:
2464:
2459:
2454:
2449:
2444:
2439:
2434:
2429:
2424:
2419:
2413:
2411:
2407:
2406:
2404:
2403:
2402:
2401:
2391:
2390:
2389:
2379:
2374:
2369:
2364:
2363:
2362:
2352:
2347:
2341:
2339:
2335:
2334:
2327:
2326:
2319:
2312:
2304:
2298:
2297:
2290:
2289:External links
2287:
2285:
2284:
2231:
2170:
2117:
2097:
2057:
1998:
1969:(4): 253–402.
1953:
1912:
1850:
1801:
1774:(4): 267–276.
1768:Nature Physics
1758:
1686:
1640:
1585:Edwards, E. E.
1575:
1513:
1451:
1386:
1341:Edwards, E. E.
1331:
1304:Nature Physics
1290:
1225:
1174:Rev. Mod. Phys
1164:
1139:
1074:
1049:
976:
949:(4): 264–266.
943:Nature Physics
926:
875:
863:
818:(12): 120501.
802:
765:(2): 581–603.
749:
712:(2): 359–371.
696:
675:
640:(6): 467–488.
620:
598:10.1.1.45.9310
561:
529:
455:
413:
367:
365:
362:
361:
360:
355:
350:
343:
340:
332:Mott insulator
315:
312:
271:ultracold atom
266:
263:
247:and geometry.
235:quantum magnet
223:beryllium ions
200:
197:
146:
143:
128:quantum system
97:Turing machine
89:Turing machine
55:quantum system
15:
9:
6:
4:
3:
2:
3512:
3511:
3500:
3497:
3496:
3494:
3479:
3478:
3469:
3468:
3465:
3455:
3452:
3450:
3447:
3445:
3442:
3440:
3437:
3433:
3432:Plasma window
3430:
3429:
3428:
3425:
3423:
3420:
3418:
3415:
3413:
3410:
3408:
3405:
3404:
3402:
3398:
3392:
3391:teleportation
3389:
3387:
3384:
3382:
3379:
3377:
3374:
3372:
3369:
3367:
3364:
3362:
3359:
3357:
3354:
3352:
3349:
3347:
3344:
3342:
3339:
3337:
3334:
3332:
3329:
3327:
3324:
3322:
3319:
3317:
3314:
3312:
3309:
3307:
3304:
3302:
3299:
3297:
3294:
3292:
3289:
3285:
3282:
3281:
3280:
3277:
3275:
3272:
3270:
3267:
3265:
3262:
3260:
3257:
3255:
3252:
3250:
3247:
3245:
3242:
3240:
3237:
3236:
3234:
3232:
3228:
3225:
3221:
3217:
3210:
3205:
3203:
3198:
3196:
3191:
3190:
3187:
3175:
3167:
3165:
3157:
3156:
3153:
3147:
3144:
3142:
3139:
3137:
3134:
3132:
3129:
3127:
3123:
3120:
3118:
3114:
3110:
3107:
3106:
3104:
3102:
3096:
3086:
3083:
3081:
3078:
3076:
3073:
3071:
3068:
3067:
3065:
3063:
3059:
3053:
3050:
3048:
3045:
3043:
3042:Spin qubit QC
3040:
3038:
3035:
3034:
3032:
3029:
3025:
3019:
3016:
3014:
3011:
3010:
3008:
3006:
3002:
2996:
2993:
2991:
2988:
2986:
2983:
2981:
2978:
2977:
2975:
2973:
2969:
2966:
2960:
2954:
2951:
2947:
2946:
2942:
2940:
2937:
2935:
2932:
2930:
2927:
2925:
2922:
2920:
2917:
2915:
2912:
2910:
2907:
2906:
2904:
2903:
2901:
2899:
2893:
2887:
2884:
2882:
2879:
2875:
2872:
2871:
2870:
2867:
2863:
2860:
2859:
2858:
2855:
2851:
2850:cluster state
2848:
2847:
2846:
2843:
2841:
2838:
2836:
2833:
2832:
2830:
2828:
2822:
2814:
2810:
2806:
2804:
2800:
2796:
2795:
2794:
2791:
2787:
2784:
2783:
2782:
2779:
2777:
2774:
2772:
2769:
2768:
2766:
2760:
2754:
2751:
2749:
2746:
2744:
2741:
2739:
2736:
2734:
2731:
2730:
2728:
2726:
2720:
2714:
2711:
2709:
2706:
2704:
2701:
2699:
2696:
2694:
2691:
2689:
2686:
2684:
2681:
2679:
2676:
2674:
2671:
2669:
2666:
2664:
2661:
2659:
2658:Deutsch–Jozsa
2656:
2654:
2651:
2649:
2646:
2644:
2641:
2640:
2638:
2636:
2632:
2622:
2619:
2615:
2612:
2610:
2607:
2605:
2602:
2601:
2600:
2597:
2595:
2594:Quantum money
2592:
2590:
2587:
2585:
2582:
2581:
2579:
2577:
2573:
2567:
2564:
2560:
2557:
2556:
2555:
2552:
2548:
2545:
2544:
2543:
2540:
2538:
2535:
2533:
2530:
2528:
2525:
2521:
2518:
2516:
2513:
2512:
2511:
2508:
2507:
2505:
2503:communication
2499:
2493:
2490:
2488:
2485:
2483:
2480:
2478:
2475:
2473:
2470:
2468:
2465:
2463:
2460:
2458:
2455:
2453:
2450:
2448:
2445:
2443:
2440:
2438:
2435:
2433:
2430:
2428:
2425:
2423:
2420:
2418:
2415:
2414:
2412:
2408:
2400:
2397:
2396:
2395:
2392:
2388:
2385:
2384:
2383:
2380:
2378:
2375:
2373:
2370:
2368:
2365:
2361:
2358:
2357:
2356:
2353:
2351:
2348:
2346:
2343:
2342:
2340:
2336:
2332:
2325:
2320:
2318:
2313:
2311:
2306:
2305:
2302:
2296:
2293:
2292:
2280:
2276:
2272:
2268:
2264:
2260:
2255:
2250:
2247:(1): 011016.
2246:
2242:
2235:
2227:
2223:
2219:
2215:
2211:
2207:
2203:
2199:
2194:
2189:
2185:
2181:
2174:
2166:
2162:
2158:
2154:
2150:
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2132:
2128:
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2104:
2100:
2094:
2090:
2086:
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2076:
2072:
2068:
2061:
2053:
2049:
2044:
2039:
2035:
2031:
2026:
2021:
2018:(5): 053010.
2017:
2013:
2009:
2002:
1994:
1990:
1986:
1982:
1977:
1972:
1968:
1964:
1957:
1949:
1945:
1940:
1935:
1931:
1927:
1923:
1916:
1908:
1904:
1900:
1896:
1892:
1888:
1884:
1880:
1875:
1870:
1866:
1862:
1854:
1846:
1842:
1837:
1832:
1828:
1824:
1820:
1816:
1812:
1805:
1797:
1793:
1789:
1785:
1781:
1777:
1773:
1769:
1762:
1747:
1743:
1739:
1735:
1731:
1727:
1723:
1719:
1714:
1709:
1705:
1701:
1697:
1690:
1682:
1678:
1674:
1670:
1665:
1660:
1657:(1): 014004.
1656:
1652:
1644:
1636:
1632:
1628:
1624:
1620:
1616:
1612:
1608:
1603:
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1579:
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1476:
1471:
1467:
1463:
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1439:
1435:
1431:
1427:
1423:
1419:
1414:
1409:
1405:
1401:
1397:
1396:Edwards, E.E.
1390:
1382:
1378:
1374:
1370:
1366:
1362:
1358:
1354:
1350:
1346:
1342:
1335:
1326:
1321:
1317:
1313:
1309:
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1301:
1294:
1286:
1282:
1278:
1274:
1270:
1266:
1262:
1258:
1253:
1248:
1244:
1240:
1232:
1230:
1221:
1217:
1213:
1209:
1205:
1201:
1197:
1193:
1188:
1183:
1180:(4): 025001.
1179:
1175:
1168:
1154:
1150:
1143:
1135:
1131:
1127:
1123:
1119:
1115:
1111:
1107:
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1085:
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1037:
1033:
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1025:
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1017:
1013:
1009:
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287:Rydberg atom
268:
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240:laser pulses
227:Penning trap
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216:quantum bits
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182:entanglement
175:, wherein a
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132:quantum bits
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3336:logic clock
3321:information
3296:electronics
3101:programming
3080:Phase qubit
2985:Circuit QED
2457:No-deleting
2399:cloud-based
1394:Islam, R.;
208:trapped-ion
31:structure.
3341:logic gate
3239:algorithms
3141:libquantum
3075:Flux qubit
2980:Cavity QED
2929:Bacon–Shor
2919:stabilizer
2447:No-cloning
2254:1607.06895
2193:1807.11342
2112:2020-05-25
2080:1511.03569
2025:1512.07329
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1158:2022-03-11
1101:2104.04119
1068:2021-12-27
1003:2102.01695
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449:2013-02-22
364:References
289:arrays in
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3386:simulator
3274:computing
3244:amplifier
3047:NV center
2482:Threshold
2462:No-hiding
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2140:1402.1388
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1028:0036-8075
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2360:timeline
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231:electron
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3361:network
3346:machine
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3264:circuit
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3099:Quantum
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2896:Quantum
2824:Quantum
2753:PostBQP
2723:Quantum
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2501:Quantum
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