1932

Abstract

We review the development of generative modeling techniques in machine learning for the purpose of reconstructing real, noisy, many-qubit quantum states. Motivated by its interpretability and utility, we discuss in detail the theory of the restricted Boltzmann machine. We demonstrate its practical use for state reconstruction, starting from a classical thermal distribution of Ising spins, then moving systematically through increasingly complex pure and mixed quantum states. We review recent techniques in reconstruction of a cold atom wavefunction, intended for use on experimental noisy intermediate-scale quantum (NISQ) devices. Finally, we discuss the outlook for future experimental state reconstruction using machine learning in the NISQ era and beyond.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-conmatphys-031119-050651
2020-03-10
2024-06-17
Loading full text...

Full text loading...

/deliver/fulltext/conmatphys/11/1/annurev-conmatphys-031119-050651.html?itemId=/content/journals/10.1146/annurev-conmatphys-031119-050651&mimeType=html&fmt=ahah

Literature Cited

  1. 1. 
    Preskill J 2018. Quantum 2:79
    [Google Scholar]
  2. 2. 
    Bernien H, Schwartz S, Keesling A, Levine H, Omran A et al. 2017. Nature 551:579–84
    [Google Scholar]
  3. 3. 
    Kandala A, Mezzacapo A, Temme K, Takita M, Brink M et al. 2017. Nature 549:242–46
    [Google Scholar]
  4. 4. 
    Zhang J, Pagano G, Hess PW, Kyprianidis A, Becker P et al. 2017. Nature 551:601–4
    [Google Scholar]
  5. 5. 
    Terhal BM 2018. Nat. Phys. 14:530–31
    [Google Scholar]
  6. 6. 
    Mazurenko A, Chiu CS, Ji G, Parsons MF, Kanász-Nagy M et al. 2017. Nature 545:462–66
    [Google Scholar]
  7. 7. 
    Islam R, Ma R, Preiss PM, Tai ME, Lukin A et al. 2015. Nature 528:77–83
    [Google Scholar]
  8. 8. 
    LeCun Y, Bengio Y, Hinton G 2015. Nature 521:436–44
    [Google Scholar]
  9. 9. 
    Rumelhart DE, McClelland JL, PDP Research Group 1986. Parallel Distributed Processing: Explorations in the Microstructure of Cognition 1 Foundations Cambridge, MA: MIT Press
    [Google Scholar]
  10. 10. 
    Rosenblatt F 1958. Psychol. Rev. 65:386–408
    [Google Scholar]
  11. 11. 
    McCulloch WS, Pitts W 1943. Bull. Math. Biophys. 5:115–33
    [Google Scholar]
  12. 12. 
    Minsky M, Papert SA 1969. Perceptrons: An Introduction to Computational Geometry Cambridge, MA: MIT Press
    [Google Scholar]
  13. 13. 
    Rumelhart DE, Hinton GE, Williams RJ 1986. Nature 323:533–36
    [Google Scholar]
  14. 14. 
    Ackley DH, Hinton GE, Sejnowski TJ 1985. Cogn. Sci. 9:147–69
    [Google Scholar]
  15. 15. 
    Little W 1974. Math. Biosci. 19:101–20
    [Google Scholar]
  16. 16. 
    Little W, Shaw GL 1978. Math. Biosci. 39:281–90
    [Google Scholar]
  17. 17. 
    Hopfield JJ 1982. PNAS 79:2554–58
    [Google Scholar]
  18. 18. 
    Shatz CJ 1992. Sci. Am. 267:360–67
    [Google Scholar]
  19. 19. 
    Hopfield JJ, Feinstein DI, Palmer RG 1983. Nature 304:158–59
    [Google Scholar]
  20. 20. 
    Hinton GE, Sejnowski TJ 1986. See Reference 9 282–317
  21. 21. 
    Smolensky P 1986. See Reference 9 194–281
  22. 22. 
    Le Roux N, Bengio Y 2008. Neural Comput. 20:1631–49
    [Google Scholar]
  23. 23. 
    Fischer A, Igel C 2012. Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications L Alvarez, M Mejail, L Gomez, J Jacobo14–36 Berlin/Heidelberg: Springer
    [Google Scholar]
  24. 24. 
    Hinton GE 2002. Neural Comput. 14:1771–800
    [Google Scholar]
  25. 25. 
    Bengio Y, Delalleau O 2009. Neural Comput. 21:1601–21
    [Google Scholar]
  26. 26. 
    Fischer A, Igel C 2011. Neural Comput. 23:664–73
    [Google Scholar]
  27. 27. 
    Carreira-Perpiñán , Hinton GE 2005. AISTATS 2005: Proceedings of the Tenth International Workshop on Artificial Intelligence and Statistics, Barbados, January 6–8 R Cowell, Z Ghahramani 33–40 New Jersey: Soc. Artif. Intell. Stat.
    [Google Scholar]
  28. 28. 
    Sutskever I, Martens J, Dahl G, Hinton G 2013. Proceedings of Machine Learning Research. Volume 28: International Conference on Machine Learning, June 17--19, 2013, Atlanta, Georgia, USA1139–47 http://proceedings.mlr.press/v28/
    [Google Scholar]
  29. 29. 
    Zeiler MD 2012. arXiv:1212.5701
  30. 30. 
    Kingma DP, Ba J 2014. arXiv:1412.6980
  31. 31. 
    Krogh A, Hertz JA 1992.Advances in Neural Information Processing Systems 4 JE Moody, SJ Hanson, RP Lippmann950–57 https://papers.nips.cc/paper/563-a-simple-weight-decay-can-improve-generalization
  32. 32. 
    Hinton GE 2012. Neural Networks: Tricks of the Trade G Montavon, GB Orr, KR Müller 599–619 Berlin/Heidelberg: Springer. 2nd ed.
    [Google Scholar]
  33. 33. 
    Vogel K, Risken H 1989. Phys. Rev. A 40:2847–49
    [Google Scholar]
  34. 34. 
    Ježek M, Fiurášek J, Hradil Z 2003. Phys. Rev. A 68:012305
    [Google Scholar]
  35. 35. 
    Banaszek K, Cramer M, Gross D 2013. New J. Phys. 15:125020
    [Google Scholar]
  36. 36. 
    James DFV, Kwiat PG, Munro WJ, White AG 2001. Phys. Rev. A 64:052312
    [Google Scholar]
  37. 37. 
    Häffner H, Hänsel W, Roos CF, Benhelm J, Chek-al-kar D et al. 2005. Nature 438:643–46
    [Google Scholar]
  38. 38. 
    Cramer M, Plenio MB, Flammia ST, Somma R, Gross D et al. 2010. Nat. Commun. 1:149
    [Google Scholar]
  39. 39. 
    Lanyon BP, Maier C, Holzäpfel M, Baumgratz T, Hempel C et al. 2017. Nat. Phys. 13:1158–62
    [Google Scholar]
  40. 40. 
    Tóth G, Wieczorek W, Gross D, Krischek R, Schwemmer C, Weinfurter H 2010. Phys. Rev. Lett. 105:250403
    [Google Scholar]
  41. 41. 
    Moroder T, Hyllus P, Tóth G, Schwemmer C, Niggebaum A et al. 2012. New J. Phys. 14:105001
    [Google Scholar]
  42. 42. 
    Gross D, Liu YK, Flammia ST, Becker S, Eisert J 2010. Phys. Rev. Lett. 105:150401
    [Google Scholar]
  43. 43. 
    Torlai G 2018. Augmenting quantum mechanics with artificial intelligence. PhD Thesis, Univ. Waterloo, Waterloo, Ontario, Canada https://uwspace.uwaterloo.ca/handle/10012/14196
    [Google Scholar]
  44. 44. 
    Torlai G, Melko RG 2016. Phys. Rev. B 94:165134
    [Google Scholar]
  45. 45. 
    Hastings WK 1970. Biometrika 57:97–109
    [Google Scholar]
  46. 46. 
    Morningstar A, Melko RG 2017. J. Mach. Learn. Res. 18:5975–91
    [Google Scholar]
  47. 47. 
    Hinton GE, Osindero S, Tehs W 2006. Neural Comput. 18:1527–54 PMID:16764513
    [Google Scholar]
  48. 48. 
    Salakhutdinov R, Hinton G 2009. Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics, Clearwater Beach, Florida, April 16–18 DA van Dyk, M Welling 5:448–55 http://proceedings.mlr.press/v5/salakhutdinov09a/salakhutdinov09a.pdf
    [Google Scholar]
  49. 49. 
    Bravyi S, Divincenzo DP, Oliveira R, Terhal BM 2008. Quantum Info. Comput. 8:361–85
    [Google Scholar]
  50. 50. 
    Torlai G, Mazzola G, Carrasquilla J, Troyer M, Melko RG, Carleo G 2018. Nat. Phys. 14:447–50
    [Google Scholar]
  51. 51. 
    Becca F, Sorella S 2017. Quantum Monte Carlo Approaches for Correlated Systems Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  52. 52. 
    Rényi A 1961. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability 1: Contributions to the Theory of Statistics, ed. J Neyman 547–61 Berkeley, Calif.: Univ. Calif. Press
    [Google Scholar]
  53. 53. 
    Hastings MB, González I, Kallin AB, Melko RG 2010. Phys. Rev. Lett. 104:157201
    [Google Scholar]
  54. 54. 
    Kallin AB, Hastings MB, Melko RG, Singh RRP 2011. Phys. Rev. B 84:165134
    [Google Scholar]
  55. 55. 
    Zhang Y, Grover T, Vishwanath A 2011. Phys. Rev. Lett. 107:067202
    [Google Scholar]
  56. 56. 
    Stéphan JM, Ju H, Fendley P, Melko RG 2013. New J. Phys. 15:015004
    [Google Scholar]
  57. 57. 
    White SR 1992. Phys. Rev. Lett. 69:2863–66
    [Google Scholar]
  58. 58. 
    Evertz HG 2003. Adv. Phys. 52:1–66
    [Google Scholar]
  59. 59. 
    Krizhevsky A, Sutskever I, Hinton GE 2012. Advances in Neural Information Processing Systems 25 F Pereira, CJC Burges, L Bottou, KQ Weinberger 1097–105 https://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks
    [Google Scholar]
  60. 60. 
    Carleo G, Troyer M 2017. Science 355:602–6
    [Google Scholar]
  61. 61. 
    Torlai G, Melko RG 2018. Phys. Rev. Lett. 120:240503
    [Google Scholar]
  62. 62. 
    Benenti G, Casati G, Strini G 2004. Principles of Quantum Computation and Information Singapore: World Sci.
    [Google Scholar]
  63. 63. 
    Hartmann MJ, Carleo G 2019. Phys. Rev. Lett. 122:250502
    [Google Scholar]
  64. 64. 
    Vicentini F, Biella A, Regnault N, Ciuti C 2019. Phys. Rev. Lett. 122:250503
    [Google Scholar]
  65. 65. 
    Nagy A, Savona V 2019. Phys. Rev. Lett. 122:250501
    [Google Scholar]
  66. 66. 
    Yoshioka N, Hamazaki R 2019. Phys. Rev. B 99:214306
    [Google Scholar]
  67. 67. 
    Carrasquilla J, Torlai G, Melko RG, Aolita L 2019. Nat. Mach. Intel. 1:155–61
    [Google Scholar]
  68. 68. 
    Torlai G, Timar B, van Nieuwenburg EPL, Levine H, Omran A 2019. arXiv:1904.08441
  69. 69. 
    Macarone Palmieri A, Kovlakov E, Bianchi F, Yudin D, Straupe S 2019. arXiv:1904.05902
  70. 70. 
    Endres M, Bernien H, Keesling A, Levine H, Anschuetz ER et al. 2016. Science 354:1024–27
    [Google Scholar]
  71. 71. 
    Schauß P, Zeiher J, Fukuhara T, Hild S, Cheneau M et al. 2015. Science 347:1455–58
    [Google Scholar]
  72. 72. 
    Labuhn H, Barredo D, Ravets S, de Léséleuc S, Macrì T et al. 2016. Nature 534:667–70
    [Google Scholar]
  73. 73. 
    Guardado-Sanchez E, Brown PT, Mitra D, Devakul T, Huse DA et al. 2018. Phys. Rev. X 8:021069
    [Google Scholar]
  74. 74. 
    Rocchetto A, Grant E, Strelchuk S, Carleo G, Severini S 2018. NPJ Quantum Inform. 4:28
    [Google Scholar]
  75. 75. 
    Beach MJS, De Vlugt I, Golubeva A, Huembeli P, Kulchytskyy B et al. 2019. SciPost Phys. 7:009
    [Google Scholar]
  76. 76. 
    Carleo G, Choo K, Hofmann D, Smith JET, Westerhout T et al. 2019. SoftwareX 10:100311
    [Google Scholar]
  77. 77. 
    Ma X, Jackson T, Zhou H, Chen J, Lu D et al. 2016. Phys. Rev. A 93:032140
    [Google Scholar]
/content/journals/10.1146/annurev-conmatphys-031119-050651
Loading
/content/journals/10.1146/annurev-conmatphys-031119-050651
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error