Advertisement

The Road to Quantum Computational Supremacy

  • Cristian S. CaludeEmail author
  • Elena Calude
Conference paper
  • 41 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 313)

Abstract

We present an idiosyncratic view of the race for quantum computational supremacy. Google’s approach and IBM challenge are examined. An unexpected side effect of the race is the significant progress in designing fast classical algorithms. Quantum supremacy, if achieved, won’t make classical computing obsolete.

Notes

Acknowledgements

We thank N. Allen for fruitful discussions and suggestions, specifically for insight on Feynman’s paper [41], and R. Brent, R. Goyal, L. Hemaspaandra, K. Pudenz, R. Hua, K. Svozil and an anonymous referee for excellent critical comments and suggestions. This work has been supported in part by the Quantum Computing Research Initiatives at Lockheed Martin.

References

  1. 1.
    Aaronson, S.: The limits of quantum. Sci. Am. 62–69 (2008)Google Scholar
  2. 2.
    Aaronson, S.: Shtetl-optimized – \(2^n\) is exponential, but \(2^{50}\) is finite (2017). https://www.scottaaronson.com/blog/?p=3512
  3. 3.
    Aaronson, S.: Why Google’s quantum supremacy milestone matters. The New York Times (2019). https://www.nytimes.com/2019/10/30/opinion/google-quantum-computer-sycamore.html
  4. 4.
    Aaronson, S., Chen, L.: Complexity-theoretic foundations of quantum supremacy experiments. Technical report No. 200, Electronic Colloquium on Computational Complexity (2016)Google Scholar
  5. 5.
    Abbott, A.A.: The Deutsch-Jozsa problem: De-quantisation and entanglement. Nat. Comput. 11(1), 3–11 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Abbott, A.A.: De-quantisation of the quantum Fourier transform. Appl. Math. Comput. 291(1), 3–13 (2012)zbMATHGoogle Scholar
  7. 7.
    Abbott, A.A., Calude, C.S.: Understanding the quantum computational speed-up via de-quantisation. EPTCS 26, 1–12 (2010)CrossRefGoogle Scholar
  8. 8.
    Abbott, A.A., Calude, C.S.: Limits of quantum computing: a sceptic’s view (presented by Jon Borwein). Quantum for quants (2016). http://www.quantumforquants.org/quantum-computing/limits-of-quantum-computing/
  9. 9.
    Abbott, A.A., Calude, C.S., Dinneen, M.J., Hua, R.: A hybrid quantum-classical paradigm to mitigate embedding costs in quantum annealing. Int. J. Quantum Inf. 1950042, 40 (2019)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Ackermann, W.: On Hilbert’s construction of the real numbers. Math. Ann. 99, 118 (1928)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Aharonov, D., Ben-Or, M., Eban, E., Mahadev, U.: Interactive proofs for quantum computations (2017). https://arxiv.org/abs/1704.04487
  12. 12.
    Allen, N.: Email to C. S. Calude. Accessed 19 Nov 2017Google Scholar
  13. 13.
    Allen, E.H., Calude, C.S.: Quassical computing. Int. J. Unconv. Comput. 14, 43–57 (2018)Google Scholar
  14. 14.
    Arute, F., Arya, K., Babbush, R., Bacon, D., Bardin, J.C., Barends, R., Biswas, R., Boixo, S., Brandao, F.G.S.L., Buell, D.A., Burkett, B., Chen, Y., Chen, Z., Chiaro, B., Collins, R., Courtney, W., Dunsworth, A., Farhi, E., Foxen, B., Fowler, A., Gidney, C., Giustina, M., Graff, R., Guerin, K., Habegger, S., Harrigan, M.P., Hartmann, M.J., Ho, A., Hoffmann, M., Huang, T., Humble, T.S., Isakov, S.V., Jeffrey, E., Jiang, Z., Kafri, D., Kechedzhi, K., Kelly, J., Klimov, P.V., Knysh, S., Korotkov, A., Kostritsa, F., Landhuis, D., Lindmark, M., Lucero, E., Lyakh, D., Mandrá, S., McClean, J.R., McEwen, M., Megrant, A., Mi, X., Michielsen, K., Mohseni, M., Mutus, J., Naaman, O., Neeley, M., Neill, C., Niu, M.Y., Ostby, E., Petukhov, A., Platt, J.C., Quintana, C., Rieffel, E.G., Roushan, P., Rubin, N.C., Sank, D., Satzinger, K.J., Smelyanskiy, V., Sung, K.J., Trevithick, M.D., Vainsencher, A., Villalonga, B., White, T., Yao, Z.J., Yeh, P., Zalcman, A., Neven, H., Martinis, J.M.: Quantum supremacy using a programmable superconducting processor. Nature 574, 505–510 (2019)CrossRefGoogle Scholar
  15. 15.
    Ball, P.: The era of quantum computing is here. Outlook: Cloudy, Quanta Magazine (2018). https://www.quantamagazine.org/the-era-of-quantum-computing-is-here-outlook-cloudy-20180124
  16. 16.
    Beaudry, N.J., Renner, R.: An intuitive proof of the data processing inequality. Quantum Inf. Comput. 12(5–6), 432–441 (2012)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Becker, A.: What Is Real? The Unfinished Quest for the Meaning of Quantum Physics. Basic Books, New York (2018)Google Scholar
  18. 18.
    Bernien, H., Schwartz, S., Keesling, A., Levine, H., Omran, A., Pichler, H., Choi, S., Zibrov, A.S., Endres, M., Greiner, M., Vuletić, V., Lukin, M.D.: Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579, EP –, 11 (2017)Google Scholar
  19. 19.
    Bernstein, D.J., Heninger, N., Lou, P., Valenta, L.: Post-quantum RSA (2017). https://cr.yp.to/papers/pqrsa-20170419.pdf
  20. 20.
    Bernstein, E., Vazirani, U.: Quantum complexity theory. In: Proceedings of the 25th Annual ACM Symposium on Theory of Computing, San Diego, California, 16–18 May 1993, pp. 11–20. ACM Press (1993)Google Scholar
  21. 21.
    Berthiaume, A., Brassard, G.: Oracle quantum computing. J. Mod. Opt. 41, 195–199 (1992)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Boixo, S., Isakov, S.V., Smelyanskiy, V.N., Babbush, R., Ding, N., Jiang, Z., Bremner, M.J., Martinis, J.M., Neven, H.: Characterizing quantum supremacy in near-term devices (2017). arXiv:1608.00263 [quant-ph]
  23. 23.
    Boixo, S., Isakov, S.V., Smelyanskiy, V.N., Neven, H.: Simulation of low-depth quantum circuits as complex undirected graphical models (2018). https://arxiv.org/pdf/1712.05384.pdf
  24. 24.
    Bravyi, S., Gosset, D., Köning, R.: Quantum advantage with shallow circuits. Science 362, 308–311 (2018)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Broadbent, A.: How to verify a quantum computation. Theory Comput. 14, 1–37 (2018)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Browne, D.E.: Efficient classical simulation of the quantum Fourier transform. New J. Phys. 9(5), 146 (2007)CrossRefGoogle Scholar
  27. 27.
    Calude, C.: Super-exponentials nonprimitive recursive, but rudimentary. Inf. Process. Lett. 25(5), 311–316 (1987)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Calude, C.S.: De-quantizing the solution of Deutsch’s problem. Int. J. Quantum Inf. 5(3), 409–415 (2007)CrossRefGoogle Scholar
  29. 29.
    Calude, C.S., Calude, E., Dinneen, M.J.: Adiabatic quantum computing challenges. ACM SIGACT News 46(1), 40–61 (2015)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Calude, C.S., Dinneen, M.J., Dumitrescu, M., Svozil, K.: Experimental evidence of quantum randomness incomputability. Phys. Rev. A 82(2), 022102 (2010)CrossRefGoogle Scholar
  31. 31.
    Calude, C.S., Dinneen, M.J., Hua, R.: QUBO formulations for the graph isomorphism problem and related problems. Theor. Comput. Sci. 1950042–40 (2019).  https://doi.org/10.1142/S0219749919500424
  32. 32.
    Campbell, E.: Random compiler for fast Hamiltonian simulation. Phys. Rev. Lett. 123, 070503 (2019)CrossRefGoogle Scholar
  33. 33.
    Chaitin, G.J., Schwartz, J.T.: A note on Monte Carlo primality tests and algorithmic information theory. Commun. Pure Appl. Math. 31(4), 521–527 (1978)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley, New York (1991)CrossRefGoogle Scholar
  35. 35.
  36. 36.
    Davis, M.: Interview with Martin Davis. Not. Am. Math. Soc. 55(560–571) (2008)Google Scholar
  37. 37.
    Deutsch, D.: Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci (1934–1990) 400(1818), 97–117 (1985)Google Scholar
  38. 38.
    Editorial: A precarious milestone for quantum computing quantum computing will suffer if supremacy is overhyped. Everyday quantum computers are still decades away. Nature 574, 453–454 (2019)Google Scholar
  39. 39.
    European flagship quantum programme (2017)Google Scholar
  40. 40.
    Edison supercomputer in TOP 500 ranking (2017). https://www.top500.org/list/2017/06/?page=1
  41. 41.
    Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Fürer, M.: Solving NP-Complete problems with quantum search. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds.) LATIN 2008: Theoretical Informatics. LNCS, vol. 4957, pp. 784–792. Springer, Berlin (2008)Google Scholar
  43. 43.
    Griffiths, R., Niu, C.: Semiclassical Fourier transform for quantum computation. Phys. Rev. Lett. 76(17), 3228–3231 (1996)CrossRefGoogle Scholar
  44. 44.
    Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on the Theory of Computing, pp. 212–219. ACM Press (1996)Google Scholar
  45. 45.
    Gruska, J.: Quantum Computing. McGraw-Hill, London (1999)zbMATHGoogle Scholar
  46. 46.
    Harrow, A.W., Montanaro, A.: Quantum computational supremacy. Nature 549(7671), 203–209 (2017)CrossRefGoogle Scholar
  47. 47.
    Havean, D.: Beware quantum winter. Google’s quantum breakthrough is the first step on a long road. Let’s make sure we don’t stumble. New Scientist, p. 21. Accessed 2 Nov 2019Google Scholar
  48. 48.
    Hemaspaandra, E., Hemaspaandra, L.A., Zimand, M.: Almost-everywhere superiority for quantum polynomial time. Inf. Comput. 175(2), 171–181 (2002)MathSciNetCrossRefGoogle Scholar
  49. 49.
    IBM builds 50-qubit quantum computer (2017). http://techvibesnow.com/ibm-builds-50-qubit-quantum-computer/
  50. 50.
    Ignatius, D.: The Quantum Spy. W. W. Norton, New York (2018)Google Scholar
  51. 51.
    Johansson, N., Larsson, J.-Å.: Efficient classical simulation of the Deutsch-Jozsa and Simon’s algorithms. Quantum Inf. Process. 16(9), 233 (2017)MathSciNetCrossRefGoogle Scholar
  52. 52.
    Johansson, N., Larsson, J.-Å.: Quantum simulation logic, oracles, and the quantum advantage. Entropy 21(8), 800 (2019)MathSciNetCrossRefGoogle Scholar
  53. 53.
    Kalai, G.: How quantum computers fail: quantum codes, correlations in physical systems, and noise accumulation (2011). arXiv:1106.0485 [quant-ph]
  54. 54.
    Kendon, V.M., Nemoto, K., Munro, W.J.: Quantum analogue computing. Philos. Trans. R. Soc. Lond. A: Math. Phys. Eng. Sci. 368(1924), 3609–3620 (2010)MathSciNetCrossRefGoogle Scholar
  55. 55.
    Kerenidis, I., Prakash, A.: Quantum recommendation system. In: Papadimitrou, C.H. (ed.) 8th Innovations in Theoretical Computer Science Conference (ITCS 2017), pp. 49:1–49:21. Dagstuhl Publishing, Germany, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)Google Scholar
  56. 56.
    Krzanich, B.: 2018 CES: Intel advances quantum and neuromorphic computing research (2018). https://newsroom.intel.com/news/intel-advances-quantum-neuromorphic-computing-research/
  57. 57.
    Lakatos, I.: Falsification and the methodology of scientific research programmes. In: Can Theories be Refuted?, pp. 59–60. Springer, Dordrecht (1976)Google Scholar
  58. 58.
    Lakatos, I.: Falsification and the methodology of scientific research programmes. In: The Methodology of Scientific Research Programmes. Philosophical Papers Volume 1. Cambridge University Press, Cambridge (1978). Online publication (2012)Google Scholar
  59. 59.
    Lanzagorta, M., Uhlmann, J.K.: Hybrid quantum-classical computing with applications to computer graphics. In: ACM SIGGRAPH 2005 Courses, SIGGRAPH ’05. ACM, New York (2005)Google Scholar
  60. 60.
    Lipton, R.J., Regan, K.W.: Quantum supremacy at last? https://rjlipton.wordpress.com/2019/10/27/quantum-supremacy-at-last/. Accessed 27 Oct 2019
  61. 61.
    Lloyd, S.: Universal quantum simulators. Science 273(5278), 1073–1078 (1996)MathSciNetCrossRefGoogle Scholar
  62. 62.
    Manin, Y.I.: Vychislimoe i nevychislimoe [Computable and Noncomputable] (in Russian). Sov. Radio. 13–15 (1980). (Last assecced 30 Nov 2017). http://www.worldcat.org/title/vychislimoe-i-nevychislimoe/oclc/11674220
  63. 63.
  64. 64.
    Mermin, N.D.: What is wrong with this pillow? Phys. Today 42(4), 9 (1989)CrossRefGoogle Scholar
  65. 65.
    Mohseni, M., Read, P., Neven, H., Boixo, S., Denchevand, V., Babbushand, R., Fowler, A., Smelyanskiy, V., Martinis, J.: Commercialize early quantum technologies. Nature 543, 171–174 (2017)CrossRefGoogle Scholar
  66. 66.
    Montanaro, A.: Quantum algorithms: an overview. Npj Quantum Inf. 2, 15023, EP –, 01 (2016)Google Scholar
  67. 67.
    Neill, C., Roushan, P., Kechedzhi, K., Boixo, S., Isakov, S.V., Smelyanskiy, V., Barends, R., Burkett, B., Chen, Y., Chen, Z., Chiaro, B., Dunsworth, A., Fowler, A., Foxen, B., Graff, R., Jeffrey, E., Kelly, J., Lucero, E., Megrant, A., Mutus, J., Neeley, M., Quintana, C., Sank, D., Vainsencher, A., Wenner, J., White, T.C., Neven, H., Martinis, J.M.: A blueprint for demonstrating quantum supremacy with superconducting qubits. arXiv:1709.06678 [quant-ph]
  68. 68.
    Nene, M.J., Upadhyay, G.: Shor’s algorithm for quantum factoring. In: Choudhary, R.K., Mandal, J.K., Auluck, N., Nagarajaram, H.A. (eds.) Advanced Computing and Communication Technologies: Proceedings of the 9th ICACCT, 2015, pp. 325–331. Springer Singapore, Singapore (2016)Google Scholar
  69. 69.
    Neville, A., Sparrow, C., Clifford, R., Johnston, E., Birchall, P.M., Montanaro, A., Neville, A.L.A., Sparrow, C., Clifford, R., Johnston, E., Birchall1, P.M., Montanaro4, A., Laing, A.: No imminent quantum supremacy by boson sampling (2017). https://arxiv.org/pdf/1705.00686.pdf
  70. 70.
    Pednault, E., Gambetta, J.: On “Quantum Supremacy”. https://www.ibm.com/blogs/research/2019/10/on-quantum-supremacy/. Accessed 24 Oct 2019
  71. 71.
    Pednault, E., Gunnels, J.A., Nannicini, G., Horesh, L., Magerlein, T., Solomonik, E., Wisnieff, R.: Breaking the 49-qubit barrier in the simulation of quantum circuits (2017). https://arxiv.org/abs/1710.05867
  72. 72.
    Preskill, J.: Quantum computing and the entanglement frontier. In: Gross, D., Henneaux, M., Sevrin, A. (eds.) The Theory of the Quantum World, pp. 63–80. World Scientific Publishing, Singapore (2012). arXiv:1203.5813 [quant-ph]
  73. 73.
    Prreskill, J.: BES Roundtable on quantum computing opportunities in chemical and materials sciences. http://www.theory.caltech.edu/~preskill/talks/DOE_BES_2017_Preskill.pdf. Accessed 31 Oct 2017
  74. 74.
    Preskill, J.: Quantum computing in the NISQ era and beyond (2018). https://arxiv.org/abs/1801.00862
  75. 75.
    Preskill, J.: Why I Called It ‘Quantum Supremacy’ (2019). https://www.quantamagazine.org/john-preskill-explains-quantum-supremacy-20191002/
  76. 76.
    Quantum algorithm zoo (2017). http://math.nist.gov/quantum/zoo/
  77. 77.
    Quantum advantage. The quantum pontiff (2017). http://dabacon.org/pontiff/?p=11863
  78. 78.
  79. 79.
    Reynolds, M.: Google on track for quantum computer breakthrough by end of 2017 (2017). https://www.newscientist.com/article/2138373-google-on-track-for-quantum-computer-breakthrough-by-end-of-2017/
  80. 80.
    Shamir, A.: Factoring numbers in O\((\log n)\) arithmetic steps. Inf. Process. Lett. 8(1), 28–31 (1979)MathSciNetCrossRefGoogle Scholar
  81. 81.
    Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings of the 35th Annual Symposium of on Foundations of Computer Science, Santa Fe, NM, 20–22 Nov 1994. IEEE Computer Society Press (1994). arXiv:quant-ph/9508027
  82. 82.
    Shor, P.W.: Why haven’t more quantum algorithms been found? J. ACM 50(1), 87–90 (2003)MathSciNetCrossRefGoogle Scholar
  83. 83.
    Simon, D.: On the power of quantum computation. SIAM J. Comput. 26(5), 1474–1483 (1997)MathSciNetCrossRefGoogle Scholar
  84. 84.
    Sipser, M.: Introduction to the Theory of Computation, 1st edn. International Thomson Publishing (1996); 3rd edn. (2013)Google Scholar
  85. 85.
    Svozil, K.: Quantum hocus-pocus. Ethics Sci. Environ. Polit. (ESEP) 16(1), 25–30 (2016)MathSciNetCrossRefGoogle Scholar
  86. 86.
    Takeda, S., Furusawa, A.: Universal quantum computing with measurement-induced continuous-variable gate sequence in a loop-based architecture. Phys. Rev. Lett. 119, 120504 (2017)CrossRefGoogle Scholar
  87. 87.
    Tamma, V.: Analogue algorithm for parallel factorization of an exponential number of large integers: Ii–optical implementation. Quantum Inf. Process. 15(12), 5243–5257 (2016)MathSciNetCrossRefGoogle Scholar
  88. 88.
    Tang, E.: A quantum-inspired classical algorithm for recommendation systems. In: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, STOC 2019, pp. 217–228. ACM, New York (2019)Google Scholar
  89. 89.
    UK programme on quantum technologies (2017). http://uknqt.epsrc.ac.uk
  90. 90.
    Wheatley, M.: D-Wave debuts new 5,000-qubit quantum computer. https://siliconangle.com/2019/09/24/d-wave-debuts-new-5000-qubit-quantum-computer/. Accessed 24 Sept 2019
  91. 91.
    Wiesner, K.: The careless use of language in quantum information (2017). https://arxiv.org/abs/1705.06768
  92. 92.
    Yao, A.C.-C.: Classical physics and the Church-Turing thesis. J. ACM (JACM) 50(1), 100–105 (2003)MathSciNetCrossRefGoogle Scholar
  93. 93.
    Zhang, J., Pagano, G., Hess, P.W., Kyprianidis, A., Becker, P., Kaplan, H., Gorshkov, A.V., Gong, Z.X., Monroe, C.: Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551, 601–604, 11 (2017)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of AucklandAucklandNew Zealand
  2. 2.Institute of Natural and Computational SciencesMassey University at AlbanyAucklandNew Zealand

Personalised recommendations