Quantum simulators permit the study of quantum systems that are difficult to study in the laboratory and impossible to model with a supercomputer. In this instance, simulators are special purpose devices designed to provide insight about specific physics problems. Quantum simulators may be contrasted with generally programmable "digital" quantum computers, which would be capable of solving a wider class of quantum problems.
A universal quantum simulator is a quantum computer proposed by Yuri Manin in 1980 and Richard Feynman in 1982. Feynman showed that a classical Turing machine would experience an exponential slowdown when simulating quantum phenomena, while his hypothetical universal quantum simulator would not. David Deutsch in 1985, took the ideas further and described a universal quantum computer. In 1996, Seth Lloyd showed that a standard quantum computer can be programmed to simulate any local quantum system efficiently.
A quantum system of many particles is described by a Hilbert space whose dimension is exponentially large in the number of particles. Therefore, the obvious approach to simulate such a system requires exponential time on a classical computer. However, it is conceivable that a quantum system of many particles could be simulated by a quantum computer using a number of quantum bits similar to the number of particles in the original system. As shown by Lloyd, this is true for a class of quantum systems known as local quantum systems. This has been extended to much larger classes of quantum systems.
Quantum simulators have been realized on a number of experimental platforms, including systems of ultracold quantum gases, polar molecules, trapped ions, photonic systems, quantum dots, and superconducting circuits.
Solving physics problems
Many important problems in physics, especially low-temperature physics and many-body physics, remain poorly understood because the underlying quantum mechanics is vastly complex. Conventional computers, including supercomputers, are inadequate for simulating quantum systems with as few as 30 particles. Better computational tools are needed to understand and rationally design materials whose properties are believed to depend on the collective quantum behavior 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 parameters of the system allows the influence of various parameters to be cleanly disentangled.
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 superposition, wherein a quantum particle 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 entanglement, allowing the behavior of even physically well separated particles to be correlated.
A trapped-ion simulator, built by a team that included the NIST and reported in April 2012, can engineer and control interactions among hundreds of quantum bits (qubits). Previous endeavors were unable to go beyond 30 quantum bits. As described in the scientific journal Nature, the capability of this simulator is 10 times more than previous devices. Also, 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.
The trapped-ion simulator consists of a tiny, single-plane crystal of hundreds of beryllium ions, less than 1 millimeter in diameter, hovering inside a device called a Penning trap. The outermost electron of each ion acts as a tiny quantum magnet 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 laser pulses 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 parameters that couldn’t be changed in natural solids, such as atomic lattice spacing and geometry.
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 frustration and entanglement and Islam et al., used adiabatic quantum simulation to demonstrate the sharpening of a phase transition 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 et al. 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 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.
Ultracold Atom Simulators
Many ultracold atom experiments are examples of quantum simulators. These include experiments studying bosons or fermions in optical lattices, the unitary Fermi gas, Rydberg atom arrays in optical tweezers. A common thread for these experiments is the capability of realizing generic Hamiltonians, such as the Hubbard or transverse-field Ising 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 impossible to realize with conventional materials, such as the Haldane model and the Harper-Hofstadter model.
Quantum simulators using superconducting qubits fall into two main categories. First, so called quantum annealers determine ground states of certain Hamiltonians after an adiabatic ramp. This approach is sometimes called adiabatic quantum computing. Second, many systems emulate specific Hamiltonians and study their ground state properties, quantum phase transitions, or time dynamics. Several important recent results include the realization of a Mott insulator in a driven-dissipative Bose-Hubbard system and studies of phase transitions in lattices of superconducting resonators coupled to qubits.
- Johnson, Tomi H.; Clark, Stephen R.; Jaksch, Dieter (2014). "What is a quantum simulator?". EPJ Quantum Technology. 1 (10). arXiv:1405.2831. doi:10.1140/epjqt10.
- This article incorporates public domain material from the National Institute of Standards and Technology document "NIST Physicists Benchmark Quantum Simulator with Hundreds of Qubits" by Michael E. Newman. Retrieved on 2013-02-22.
- 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). "Engineered two-dimensional Ising interactions in a trapped-ion quantum simulator with hundreds of spins" (PDF). Nature. 484 (7395): 489–92. arXiv:1204.5789. Bibcode:2012Natur.484..489B. doi:10.1038/nature10981. PMID 22538611. Note: This manuscript is a contribution of the US National Institute of Standards and Technology and is not subject to US copyright.
- Manin, Yu. I. (1980). Vychislimoe i nevychislimoe [Computable and Noncomputable] (in Russian). Sov.Radio. pp. 13–15. Archived from the original on 2013-05-10. Retrieved 2013-03-04.
- Feynman, Richard (1982). "Simulating Physics with Computers". International Journal of Theoretical Physics. 21 (6–7): 467–488. Bibcode:1982IJTP...21..467F. CiteSeerX 10.1.1.45.9310. doi:10.1007/BF02650179.
- Lloyd, S. (1996). "Universal quantum simulators". Science. 273 (5278): 1073–8. Bibcode:1996Sci...273.1073L. doi:10.1126/science.273.5278.1073. PMID 8688088.
- Dorit Aharonov; Amnon Ta-Shma (2003). "Adiabatic Quantum State Generation and Statistical Zero Knowledge". arXiv:quant-ph/0301023.
- Berry, Dominic W.; Graeme Ahokas; Richard Cleve; Sanders, Barry C. (2007). "Efficient quantum algorithms for simulating sparse Hamiltonians". Communications in Mathematical Physics. 270 (2): 359–371. arXiv:quant-ph/0508139. Bibcode:2007CMaPh.270..359B. doi:10.1007/s00220-006-0150-x.
- Childs, Andrew M. (2010). "On the relationship between continuous- and discrete-time quantum walk". Communications in Mathematical Physics. 294 (2): 581–603. arXiv:0810.0312. Bibcode:2010CMaPh.294..581C. doi:10.1007/s00220-009-0930-1.
- Kliesch, M.; Barthel, T.; Gogolin, C.; Kastoryano, M.; Eisert, J. (12 September 2011). "Dissipative Quantum Church-Turing Theorem". Physical Review Letters. 107 (12): 120501. arXiv:1105.3986. Bibcode:2011PhRvL.107l0501K. doi:10.1103/PhysRevLett.107.120501. PMID 22026760.
- Nature Physics Insight – Quantum Simulation. Nature.com. April 2012.
- Cirac, J. Ignacio; Zoller, Peter (2012). "Goals and opportunities in quantum simulation" (PDF). Nature Physics. 8 (4): 264–266. Bibcode:2012NatPh...8..264C. doi:10.1038/nphys2275.
- Friedenauer, A.; Schmitz, H.; Glueckert, J. T.; Porras, D.; Schaetz, T. (27 July 2008). "Simulating a quantum magnet with trapped ions". Nature Physics. 4 (10): 757–761. Bibcode:2008NatPh...4..757F. doi:10.1038/nphys1032.
- Kim, K.; Chang, M.-S.; Korenblit, S.; Islam, R.; Edwards, E. E.; Freericks, J. K.; Lin, G.-D.; Duan, L.-M.; Monroe, C. (June 2010). "Quantum simulation of frustrated Ising spins with trapped ions". Nature. 465 (7298): 590–593. Bibcode:2010Natur.465..590K. doi:10.1038/nature09071. PMID 20520708.
- Islam, R.; Edwards, E.E.; 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". Nature Communications. 2 (1): 377. arXiv:1103.2400. Bibcode:2011NatCo...2E.377I. doi:10.1038/ncomms1374. PMID 21730958.
- Barreiro, Julio T.; Müller, 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". Nature. 470 (7335): 486–491. arXiv:1104.1146. Bibcode:2011Natur.470..486B. doi:10.1038/nature09801. PMID 21350481.
- 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". Science. 334 (6052): 57–61. arXiv:1109.1512. Bibcode:2011Sci...334...57L. doi:10.1126/science.1208001. PMID 21885735.
- Islam, R.; Senko, C.; Campbell, W. C.; Korenblit, S.; Smith, J.; Lee, A.; Edwards, E. E.; 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". Science. 340 (6132): 583–587. arXiv:1210.0142. Bibcode:2013Sci...340..583I. doi:10.1126/science.1232296. PMID 23641112.
- 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". Nature. 484 (7395): 489–492. arXiv:1204.5789. Bibcode:2012Natur.484..489B. doi:10.1038/nature10981. PMID 22538611.
- 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". Quantum Science and Technology. 4 (1): 014004. arXiv:1802.03118. doi:10.1088/2058-9565/aae0fe.
- Bloch, Immanuel; Dalibard, Jean; Nascimbene, Sylvain (2012). "Quantum simulations with ultracold quantum gases". Nature Physics. 8 (4): 267–276. doi:10.1038/nphys2259.
- Gross, Christian; Bloch, Immanuel (September 8, 2017). "Quantum simulations with ultracold atoms in optical lattices". Nature. 357 (6355): 995–1001. doi:10.1126/science.aal3837. PMID 28883070.
- Jotzu, Gregor; Messer, Michael; Desbuquois, Rémi; Lebrat, Martin; Uehlinger, Thomas; Greif, Daniel; Esslinger, Tilman (13 November 2014). "Experimental realization of the topological Haldane model with ultracold fermions". Nature. 515 (7526): 237–240. arXiv:1406.7874. doi:10.1038/nature13915. PMID 25391960.
- Simon, Jonathan (13 November 2014). "Magnetic fields without magnetic fields". Nature. 515 (7526): 202–203. doi:10.1038/515202a. PMID 25391956.
- Zhang, Dan-Wei; Zhu, Yan-Qing; Zhao, Y. X.; Yan, Hui; Zhu, Shi-Liang (29 March 2019). "Topological quantum matter with cold atoms". Advances in Physics. 67 (4): 253–402. arXiv:1810.09228. doi:10.1080/00018732.2019.1594094.
- Paraoanu, G. S. (4 April 2014). "Recent Progress in Quantum Simulation Using Superconducting Circuits". Journal of Low Temperature Physics. 175 (5–6): 633–654. arXiv:1402.1388. doi:10.1007/s10909-014-1175-8.
- 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". Nature. 566 (7742): 51–57. arXiv:1807.11342. doi:10.1038/s41586-019-0897-9. PMID 30728523.
- 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". Physical Review X. 7 (1): 011016. arXiv:1607.06895. doi:10.1103/PhysRevX.7.011016.