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Quantum simulator

In this photograph of a quantum simulator crystal the ions are fluorescing, 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 lattice structure. Credit: Britton/NIST
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 trap (not shown). Inside the trap the crystal rotates clockwise. Credit: Britton/NIST

Quantum simulators permit the study of a quantum system in a programmable fashion. In this instance, simulators are special purpose devices designed to provide insight about specific physics problems.[1][2][3] 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[4] and Richard Feynman in 1982.[5]

A quantum system may be simulated by either a Turing machine or a quantum Turing machine, as a classical Turing machine is able to simulate a universal quantum computer (and therefore any simpler quantum simulator), meaning they are equivalent from the point of view of computability theory. The simulation of quantum physics by a classical computer has been shown to be inefficient.[6] In other words, quantum computers provide no additional power 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 complexity classes, which is why quantum Turing machines are useful for simulating quantum systems. This is known as quantum supremacy, the idea that there are problems only quantum Turing machines can solve in any feasible amount of time.

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.[5] This has been extended to much larger classes of quantum systems.[7][8][9][10]

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.[11]

  1. ^ 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. S2CID 120250321.
  2. ^ Public Domain This article incorporates public domain material from Michael E. Newman. NIST Physicists Benchmark Quantum Simulator with Hundreds of Qubits. National Institute of Standards and Technology. Retrieved 2013-02-22.
  3. ^ 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. S2CID 4370334. Note: This manuscript is a contribution of the US National Institute of Standards and Technology and is not subject to US copyright.
  4. ^ 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.
  5. ^ a b 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. S2CID 124545445.
  6. ^ Feynman, Richard P. (1982-06-01). "Simulating physics with computers". International Journal of Theoretical Physics. 21 (6): 467–488. Bibcode:1982IJTP...21..467F. doi:10.1007/BF02650179. ISSN 1572-9575. S2CID 124545445.
  7. ^ Dorit Aharonov; Amnon Ta-Shma (2003). "Adiabatic Quantum State Generation and Statistical Zero Knowledge". arXiv:quant-ph/0301023.
  8. ^ 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. S2CID 37923044.
  9. ^ 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. S2CID 14801066.
  10. ^ 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. S2CID 11322270.
  11. ^ Nature Physics Insight – Quantum Simulation. Nature.com. April 2012.
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