1932

Abstract

Quantum computing is widely considered a frontier of interdisciplinary research and involves fields ranging from computer science to physics and from chemistry to engineering. On the one hand, the stochastic essence of quantum physics results in the random nature of quantum computing; thus, there is an important role for statistics to play in the development of quantum computing. On the other hand, quantum computing has great potential to revolutionize computational statistics and data science. This article provides an overview of the statistical aspect of quantum computing. We review the basic concepts of quantum computing and introduce quantum research topics such as quantum annealing and quantum machine learning, which require statistics to be understood.

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2022-03-07
2024-12-02
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Literature Cited

  1. Aaronson S, Arkhipov A 2011. The computational complexity of linear optics. Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing333–42 New York: ACM
    [Google Scholar]
  2. Aaronson S, Chen L 2016. Complexity-theoretic foundations of quantum supremacy experiments. arXiv:1612.05903 [quant-ph]
  3. Adachi SH, Henderson MP. 2015. Application of quantum annealing to training of deep neural networks. arXiv:1510.06356 [quant-ph]
  4. Albash T, Rønnow TF, Troyer M, Lidar DA. 2015. Reexamining classical and quantum models for the D-Wave One processor. Eur. Phys. J. Spec. Top. 224:1111–29
    [Google Scholar]
  5. Amin MH, Andriyash E, Rolfe J, Kulchytskyy B, Melko R 2018. Quantum Boltzmann machine. Phys. Rev. X 8:2021050
    [Google Scholar]
  6. Artiles LM, Gill RD, Guţă MI. 2005. An invitation to quantum tomography. J. R. Stat. Soc. Ser. B 67:1109–34
    [Google Scholar]
  7. Arute F, Arya K, Babbush R, Bacon D, Bardin JC et al. 2019. Quantum supremacy using a programmable superconducting processor. Nature 574:7779505–10
    [Google Scholar]
  8. Barndorff-Nielsen OE, Gill RD, Jupp PE. 2003. On quantum statistical inference. J. R. Stat. Soc. Ser. B 65:4775–804
    [Google Scholar]
  9. Benedetti M, Realpe-Gómez J, Biswas R, Perdomo-Ortiz A. 2016. Estimation of effective temperatures in quantum annealers for sampling applications: a case study with possible applications in deep learning. Phys. Rev. A 94:2022308
    [Google Scholar]
  10. Bertsimas D, Tsitsiklis J. 1993. Simulated annealing. Stat. Sci. 8:110–15
    [Google Scholar]
  11. Biamonte J, Wittek P, Pancotti N, Rebentrost P, Wiebe N, Lloyd S. 2017. Quantum machine learning. Nature 549:7671195
    [Google Scholar]
  12. Boixo S, Isakov SV, Smelyanskiy VN, Babbush R, Ding N et al. 2018. Characterizing quantum supremacy in near-term devices. Nat. Phys. 14:6595
    [Google Scholar]
  13. Boixo S, Rønnow TF, Isakov SV, Wang Z, Wecker D et al. 2014. Evidence for quantum annealing with more than one hundred qubits. Nat. Phys. 10:3218
    [Google Scholar]
  14. Boixo S, Smelyanskiy VN, Shabani A, Isakov SV, Dykman M et al. 2016. Computational multiqubit tunnelling in programmable quantum annealers. Nat. Commun. 7:10327
    [Google Scholar]
  15. Bouland A, Fefferman B, Nirkhe C, Vazirani U 2018. Quantum supremacy and the complexity of random circuit sampling. arXiv:1803.04402 [quant-ph]
  16. Brady LT, van Dam W. 2016. Quantum Monte Carlo simulations of tunneling in quantum adiabatic optimization. Phys. Rev. A 93:3032304
    [Google Scholar]
  17. Brooke J, Bitko D, Aeppli G. 1999. Quantum annealing of a disordered magnet. Science 284:5415779–81
    [Google Scholar]
  18. Cai T, Kim D, Wang Y, Yuan M, Zhou HH. 2016. Optimal large-scale quantum state tomography with Pauli measurements. Ann. Stat. 44:2682–712
    [Google Scholar]
  19. Ciliberto C, Herbster M, Ialongo AD, Pontil M, Rocchetto A et al. 2018. Quantum machine learning: a classical perspective. Proc. R. Soc. A 474:220920170551
    [Google Scholar]
  20. Dunjko V, Briegel HJ. 2018. Machine learning & artificial intelligence in the quantum domain: a review of recent progress. Rep. Prog. Phys. 81:7074001
    [Google Scholar]
  21. Farhi E, Goldstone J, Gutmann S. 2002. Quantum adiabatic evolution algorithms versus simulated annealing. arXiv:quant-ph/0201031
  22. Farhi E, Goldstone J, Gutmann S, Lapan J, Lundgren A, Preda D. 2001. A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. Science 292:5516472–75
    [Google Scholar]
  23. Farhi E, Goldstone J, Gutmann S, Sipser M. 2000. Quantum computation by adiabatic evolution. arXiv:quant-ph/0001106
  24. Fischer A, Igel C 2012. An introduction to restricted Boltzmann machines. CIARP 2012: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications L Alvarez, M Mejail, L Gomez, J Jacobo 14–36 New York: Springer
    [Google Scholar]
  25. Fischer A, Igel C. 2014. Training restricted Boltzmann machines: an introduction. Pattern Recognit. 47:25–39
    [Google Scholar]
  26. Hamilton CS, Kruse R, Sansoni L, Barkhofen S, Silberhorn C, Jex I. 2017. Gaussian boson sampling. Phys. Rev. Lett. 119:17170501
    [Google Scholar]
  27. Harrow AW, Montanaro A. 2017. Quantum computational supremacy. Nature 549:7671203
    [Google Scholar]
  28. Hinton G, Salakhutdinov R 2012. A better way to pretrain deep Boltzmann machines. Advances in Neural Information Processing Systems 25 F Pereira, CJC Burges, L Bottou, KQ Weinberger 2447–55 Red Hook, NY: Curran
    [Google Scholar]
  29. Holevo AS. 2001. Statistical Structure of Quantum Theory New York: Springer
    [Google Scholar]
  30. Hu J, Wang Y. 2021. Quantum annealing via path-integral Monte Carlo with data augmentation. J. Comput. Graph. Stat. 30:284–96
    [Google Scholar]
  31. Isakov SV, Mazzola G, Smelyanskiy VN, Jiang Z, Boixo S et al. 2016. Understanding quantum tunneling through quantum Monte Carlo simulations. Phys. Rev. Lett. 117:18180402
    [Google Scholar]
  32. Jörg T, Krzakala F, Kurchan J, Maggs AC 2010. Quantum annealing of hard problems. Prog. Theor. Phys. Suppl. 184:290–303
    [Google Scholar]
  33. Kieferova M, Wiebe N. 2016. Tomography and generative data modeling via quantum Boltzmann training. arXiv:1612.05204 [quant-ph]
  34. Kirkpatrick S, Gelatt CD, Vecchi MP. 1983. Optimization by simulated annealing. Science 220:4598671–80
    [Google Scholar]
  35. Lund A, Bremner MJ, Ralph T. 2017. Quantum sampling problems, BosonSampling and quantum supremacy. NPJ Quantum Inform. 3:115
    [Google Scholar]
  36. Markov IL, Fatima A, Isakov SV, Boixo S. 2018. Quantum supremacy is both closer and farther than it appears. arXiv:1807.10749 [quant-ph]
  37. McGeoch CC. 2014. Adiabatic quantum computation and quantum annealing: theory and practice. Synth. Lect. Quantum Comput. 5:21–93
    [Google Scholar]
  38. Neill C, Roushan P, Kechedzhi K, Boixo S, Isakov SV et al. 2018. A blueprint for demonstrating quantum supremacy with superconducting qubits. Science 360:6385195–99
    [Google Scholar]
  39. Nielsen MA, Chuang IL. 2010. Quantum Computation and Quantum Information Cambridge, UK: Cambridge Univ. Press. , 10th ed..
    [Google Scholar]
  40. Parthasarathy KR. 2012. An Introduction to Quantum Stochastic Calculus Basel, Switz: Birkhäuser
    [Google Scholar]
  41. Petz D. 2008. Quantum Information Theory and Quantum Statistics New York: Springer
    [Google Scholar]
  42. Quesada N, Arrazola JM, Killoran N. 2018. Gaussian boson sampling using threshold detectors. Phys. Rev. A 98:6062322
    [Google Scholar]
  43. Rinott Y, Shoham T, Kalai G. 2020. Statistical aspects of the quantum supremacy demonstration. arXiv:2008.05177 [quant-ph]
  44. Rønnow TF, Wang Z, Job J, Boixo S, Isakov SV et al. 2014. Defining and detecting quantum speedup. Science 345:6195420–24
    [Google Scholar]
  45. Sakurai J, Napolitano J. 2017. Modern Quantum Mechanics Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  46. Salakhutdinov R. 2015. Learning deep generative models. Annu. Rev. Stat. Appl. 2:361–85
    [Google Scholar]
  47. Salakhutdinov R, Hinton G 2009. Deep Boltzmann machines. Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics D van Dyk, M Welling 448–55 Brookline, MA: Microtome
    [Google Scholar]
  48. Salakhutdinov R, Hinton G. 2012. An efficient learning procedure for deep Boltzmann machines. Neural Comput. 24:81967–2006
    [Google Scholar]
  49. Shankar R. 2012. Principles of Quantum Mechanics New York: Springer
    [Google Scholar]
  50. Sinervo PK 2003. Definition and treatment of systematic uncertainties in high energy physics and astrophysics. Proceedings of the Conference on Statistical Problems in Particle Physics, Astrophysics and Cosmology (PHYSTAT2003) L Lyons, R Mount, R Reitmeyer 122–29 Stanford, CA: SLAC
    [Google Scholar]
  51. Sutton RS, Barto AG. 2018. Reinforcement Learning: An Introduction Cambridge, MA: Bradford. , 2nd ed..
    [Google Scholar]
  52. Wang Y. 2012. Quantum computation and quantum information. Stat. Sci. 27:3373–94
    [Google Scholar]
  53. Wang Y. 2022. When quantum computation meets data science: making data science quantum. Harv. Data Sci. Rev In press
    [Google Scholar]
  54. Wang Y, Song X. 2020. Quantum science and quantum technology. Stat. Sci. 35:151–74
    [Google Scholar]
  55. Wang Y, Wu S. 2020. Asymptotic analysis via stochastic differential equations of gradient descent algorithms in statistical and computational paradigms. J. Mach. Learn. Res. 21:1991–103
    [Google Scholar]
  56. Wang Y, Wu S, Zou J. 2016. Quantum annealing with Markov chain Monte Carlo simulations and D-Wave quantum computers. Stat. Sci. 31:3362–98
    [Google Scholar]
  57. Wang Y, Xu C. 2015. Density matrix estimation in quantum homodyne tomography. Stat. Sin. 3:953–73
    [Google Scholar]
  58. Wiebe N, Kapoor A, Svore KM. 2014. Quantum deep learning. arXiv:1412.3489 [quant-ph]
  59. Wittek P. 2014. Quantum Machine Learning: What Quantum Computing Means to Data Mining New York: Academic
    [Google Scholar]
  60. Zhong HS, Wang H, Deng YH, Chen MC, Peng LC et al. 2020. Quantum computational advantage using photons. Science 370:65231460–63
    [Google Scholar]
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