DOI QR코드

DOI QR Code

The Present and Perspective of Quantum Machine Learning

양자 기계학습 기술의 현황 및 전망

  • Received : 2015.11.04
  • Accepted : 2016.04.19
  • Published : 2016.07.15

Abstract

This paper presents an overview of the emerging field of quantum machine learning which promises an innovative expedited performance of current classical machine learning algorithms by applying quantum theory. The approaches and technical details of recently developed quantum machine learning algorithms that have been able to substantially accelerate existing classical machine learning algorithms are presented. In addition, the quantum annealing algorithm behind the first commercial quantum computer is also discussed.

본고에서는 양자역학 기반의 기계학습인 양자 기계학습의 현황과 전망을 조망하고자 한다. 양자역학 기반의 양자컴퓨팅이 보여준 혁신적인 계산속도 개선에 힘입어 기계학습 분야에 양자컴퓨팅 알고리즘을 적용하는 연구는 빅데이터 시대의 도래에 따라 최근 집중적인 관심을 받고 있다. 고전적인 기계학습 알고리즘들에 양자컴퓨팅을 접목하여 획기적인 속도개선을 가능하게 하는 알고리즘 연구들과 최초의 상용 양자컴퓨터로 화제가 되고 있는 양자 담금질 알고리즘 등을 중심으로 양자 기계학습의 최신동향과 가능성을 살펴보고자 한다.

Keywords

References

  1. M. Hilbert and P. Lopez, "The world's technological capacity to store, communicate, and compute information," Science, Vol. 332, No. 6025, pp. 60-65, 2011. https://doi.org/10.1126/science.1200970
  2. P. Shor, "Algorithms for quantum computation: Discrete log and factoring," Proc. of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, USA, Nov. 22-24, pp. 124-134, 1994.
  3. S. Lloyd, M. Mohseni, and P. Rebentrost, "Quantum algorithms for supervised and unsupervised machine learning," arXiv:1307.0411, 2013.
  4. M. Johnson et al., "Quantum annealing with manufactured spins," Nature, Vol. 473, pp. 194-198, May 2011. https://doi.org/10.1038/nature10012
  5. R. Feynman, R. Leighton, and M. Sands, Lectures on Physics, Vol. III, Addison Wesley, 1965.
  6. G. Greenstein and A. Zajonc, The Quantum Challenge, Jones and Bartlett Publishers, 1997.
  7. R. Feynman, "Simulating physics with computers," International Journal of Theoretical Physics, Vol. 21, pp. 467-488, 1982. https://doi.org/10.1007/BF02650179
  8. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge: Cambridge University Press, 2010.
  9. D. Deutsch, "Quantum theory, the church-turing principle and the universal quantum computer," Proc. of the Royal Society of London, Vol. A400, pp. 97-117, 1985.
  10. L. Grover, "A fast quantum mechanical algorithm for database search," Proc. of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing, (Philadelphia, Pennsylvania), pp. 212-219, May 1996.
  11. M. Boyer, G. Brassard, P. Hoyer, and A. Tapp, "Tight bounds on quantum search," Proc. of the Workshop on Physics of Computation: PhysComp' 96, (Los Alamitos, CA), 1996.
  12. P. Shor, "Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer," SIAM Journal on Computing, Vol. 26, No. 5, pp. 1484-1509, 1997. https://doi.org/10.1137/S0097539795293172
  13. M. Ettinger, P. Hoyer, and E. Knill, "The quantum query complexity of the hidden subgroup problem is polynomial," Information Processing Letters, Vol. 91, pp. 43-48, Jul. 2004. https://doi.org/10.1016/j.ipl.2004.01.024
  14. S. Hallgren, "Polynomial-time quantum algorithms for pell's equation and the principal ideal problem," Journal of the ACM, Vol. 54, No. 4, 2007.
  15. Y. Aharonov, L. Davidovich, and N. Zagury, "Quantum random walks," Phys. Rev. A, Vol. 48, No. 2, pp. 1687-1690, 1993. https://doi.org/10.1103/PhysRevA.48.1687
  16. A. Ambainis, "Quantum walk algorithm for element distinctness," SIAM Journal on Computing, Vol. 37, No. 1, pp. 210-239, 2007. https://doi.org/10.1137/S0097539705447311
  17. B. W. Reichardt and R. Spalek, "Span-programbased quantum algorithm for evaluating formulas," Proc. of the 40th Annual ACM symposium on Theory of Computing, pp. 103-112, Association for Computing Machinery, 2008.
  18. E. Martin-Lopez, A. Laing, T. Lawson, R. Alvarez, X.-Q. Zhou, and J. L. O'Brien, "Experimental realization of shor's quantum factoring algorithm using qubit recycling," Nature Photonics, Oct. 2012.
  19. M. Schuld, I. Sinayskiy, and F. Petruccione, "An introduction to quantum machine learning," Contemporary Physics, Vol. 56, No. 2, pp. 172-185, 2015. https://doi.org/10.1080/00107514.2014.964942
  20. D. Anguita, S. Ridella, F. Rivieccio, and R. Zunino, "Quantum optimization for training support vector machines," Neural Networks, Vol. 16, No. 5, pp. 763-770, 2003. https://doi.org/10.1016/S0893-6080(03)00087-X
  21. E. Aimeur, G. Brassard, and S. Gambs, "Quantum speed-up for unsupervised learning," Machine Learning, Vol. 90, No. 2, pp. 261-287, 2013. https://doi.org/10.1007/s10994-012-5316-5
  22. N. Wiebe, A. Kapoor, and K. M. Svore, "Quantum nearest neighbor algorithms for machine learning," arXiv:1401.2142, 2014.
  23. V. Giovannetti, S. Lloyd, and L. Maccone, "Quantum random access memory," Physical Review Letters, Vol. 100, No. 160501, 2008.
  24. P. Rebentrost, M. Mohseni, and S. Lloyd, "Quantum support vector machine for big data classification," Physical Review Letters, Vol. 113, No. 130503, 2014.
  25. A. W. Harrow, A. Hassidim, and S. Lloyd, "Quantum algorithm for linear systems of equations," Physical Review Letters, Vol. 103, Oct. 2009.
  26. C. Cortes and V. Vapnik, "Support vector networks," Machine Learning, Vol. 20, pp. 273-297, 1995.
  27. Z. Li, X. Liu, N. Xu, and J. Du, "Experimental realization of a quantum support vector machine," Physical Review Letters, Vol. 114, Apr. 2015.
  28. S. Lloyd, "Least square quantization in pcm," IEEE Transactions on Information Theory, Vol. 28, No. 2, 1982.
  29. N. Wiebe, D. Braun, and S. Lloyd, "Quantum algorithm for data fitting," Physical Review Letters, Vol. 109, Aug. 2012.
  30. A. Monras, A. Beige, and K. Wiesner, "Hidden quantum markov models and nonadaptive read-out of many-body states," Applied Mathematical and Computational Sciences, Vol. 3, pp. 93-122, 2010.
  31. J. Barry, D. Barry, and S. Aaronson, "Quantum partially observable markov decision processes," Physical Review A, Vol. 90, pp. 032311-1-032311-11, 2014. https://doi.org/10.1103/PhysRevA.90.032311
  32. A. Ezhov, A. Nifanova, and D. Ventura, "Quantum associative memory with distributed queries," Information Sciences, Vol. 128, No. 271-293, 2000. https://doi.org/10.1016/S0020-0255(00)00057-8
  33. J. Howell, J. Yeazell, and D. Ventura, "Optically simulating a quantum associative memory," Physical Review A, Vol. 62, 2000.
  34. N. Wiebe, A. Kapoor, and K. M. Svore, "Quantum deep learning," arXiv:1412.3489, 2015.
  35. E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, "Quantum computation by adiabatic evolution," arXiv:quant-ph, Vol. 0405098, 2000.
  36. E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, and D. Preda, "A quantum adiabatic evolution algorithm applied to random instances of an np-complete problem," Science, Vol. 292, pp. 472-476, Apr. 2001. https://doi.org/10.1126/science.1057726
  37. D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lyold, and O. Regev, "Adiabatic quantum computation is equivalent to standard quantum computation," SIAM Journal of Computing, Vol. 37, 2007.
  38. J. Roland and J. N. Cerf, "Quantum search by local adiabatic evolution," Physical Review A, Vol. 65, 2002.
  39. V. Bapst, L. Foini, F. Krzakala, G. Semerjian, and F. Zamponi, "The quantum adiabatic algorithm applied to random optimization problems: the quantum spin glass perspective," Physics Reports, Vol. 523, No. 127, 2013.
  40. S. G. Brush, "History of the lenz-ising model," Rev. Mod. Phys., Vol. 39, Oct. 1967.
  41. F. Barahona, "On the computational complexity of ising spin glass models," Journal of Physics, Vol. A15, No. 3241, 1982.
  42. A. Lucas, "Ising formulations of many np problems," Frontiers in Physics, Vol. 2, 2014.
  43. J. D. Biamonte and P. J. Love, "Realizable hamiltonians for universal adiabatic quantum computers," Physical Review A, Vol. 78, No. 012352, 2008.
  44. J. D. Whitfield, M. Faccin, and J. D. Biamonte, "Ground state spin logic," Europhysics Letters, Vol. 99, No. 57004, 2012.
  45. T. Kadowaki and H. Nishimori, "Quantum annealing in the transverse ising model," Phys. Rev. E, Vol. 58, No. 5355, 1998.
  46. J. Brooke, D. Bitko, T. F. Rosenbaum, and G. Aeppli, "Quantum annealing of a disordered magnet," Science, Vol. 284, No. 779, 1999.
  47. M. W. Johnson et al., "Quantum annealing with manufactured spins," Nature, Vol. 473, No. 194, 2011.
  48. S. Boixo, T. F. Ronnow, S. V. Isakov, Z. Wang, D. Wecker, D. A. Lidar, J. M. Martinis, and M. Troyer, "Quantum annealing with more than one hundred qubits," Nature Phys., Vol. 10, No. 218, 2014.
  49. S. W. Shin, G. Smith, J. A. Smolin, and U. Vazirani, "How "quantum" is the d-wave machine?" arXiv: 1401.7087, 2015.
  50. A. Cho, "Quantum or not, controversial computer yields no speedup," Science, Vol. 344, Jun. 2014.
  51. H. G. Katzgraber, F. Hamze, Z. Zhu, A. J. Ochoa, and H. Munoz-Bauza, "Seeking quantum speedup through spin glasses: The good, the bad, and the ugly," Phys. Rev. X, Vol. 5, No. 031026, 2015.
  52. E. Cohen and B. Tamir, "Quantum annealing-foundations and frontiers," The European Physical Journal, Vol. 224, pp. 89-110, Feb. 2015.