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Classical simulation of universal measurement-based quantum computation using multipartite Bell scenarios (2410.23734v1)

Published 31 Oct 2024 in quant-ph

Abstract: We introduce a new classical simulation algorithm based on non-signaling polytopes of multipartite Bell scenarios, capable of simulating universal measurement-based quantum computation with single-qubit Pauli measurements. In our model, the simultaneous presence of non-stabilizerness and entanglement is necessary for quantum speedup. The region of quantum states that can be efficiently simulated includes the Bell polytope and extends beyond what is currently achievable by sampling algorithms based on phase space methods.

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References (38)
  1. D. Gottesman, “The Heisenberg representation of quantum computers,” arXiv preprint quant-ph/9807006, 1998.
  2. S. Aaronson and D. Gottesman, “Improved simulation of stabilizer circuits,” Physical Review A, vol. 70, no. 5, p. 052328, 2004.
  3. E. F. Galvao, “Discrete Wigner functions and quantum computational speedup,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 71, no. 4, p. 042302, 2005.
  4. C. Cormick, E. F. Galvao, D. Gottesman, J. P. Paz, and A. O. Pittenger, “Classicality in discrete Wigner functions,” Physical Review A—Atomic, Molecular, and Optical Physics, vol. 73, no. 1, p. 012301, 2006.
  5. V. Veitch, C. Ferrie, D. Gross, and J. Emerson, “Negative quasi-probability as a resource for quantum computation,” New Journal of Physics, vol. 14, no. 11, p. 113011, 2012.
  6. N. Delfosse, P. Allard Guerin, J. Bian, and R. Raussendorf, “Wigner function negativity and contextuality in quantum computation on rebits,” Phys. Rev. X, vol. 5, p. 021003, Apr 2015.
  7. “Contextuality and W]igner-function negativity in qubit quantum computation, author=Raussendorf, Robert and Browne, Dan E and Delfosse, Nicolas and Okay, Cihan and Bermejo-Vega, Juan, journal=Physical Review A, volume=95, number=5, pages=052334, year=2017, publisher=APS,”
  8. R. Raussendorf, J. Bermejo-Vega, E. Tyhurst, C. Okay, and M. Zurel, “Phase-space-simulation method for quantum computation with magic states on qubits,” Physical Review A, vol. 101, no. 1, p. 012350, 2020.
  9. M. Zurel, L. Z. Cohen, and R. Raussendorf, “Simulation of quantum computation with magic states via jordan-wigner transformations,” arXiv preprint arXiv:2307.16034, 2023.
  10. M. Zurel and A. Heimendahl, “Efficient classical simulation of quantum computation beyond Wigner positivity,” arXiv preprint arXiv:2407.10349, 2024.
  11. M. Zurel, C. Okay, and R. Raussendorf, “Hidden variable model for universal quantum computation with magic states on qubits,” Physical Review Letters, vol. 125, no. 26, p. 260404, 2020.
  12. M. Zurel, C. Okay, R. Raussendorf, and A. Heimendahl, “Hidden variable model for quantum computation with magic states on any number of qudits of any dimension,” arXiv preprint arXiv:2110.12318, 2021.
  13. V. Danos and E. Kashefi, “Pauli measurements are universal,” Electronic Notes in Theoretical Computer Science, vol. 170, pp. 95–100, 2007.
  14. J. Bermejo-Vega, N. Delfosse, D. E. Browne, C. Okay, and R. Raussendorf, “Contextuality as a resource for models of quantum computation with qubits,” Physical review letters, vol. 119, no. 12, p. 120505, 2017.
  15. S. Bravyi and A. Kitaev, “Universal quantum computation with ideal clifford gates and noisy ancillas,” Physical Review A, vol. 71, no. 2, p. 022316, 2005.
  16. R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Physical review letters, vol. 86, no. 22, p. 5188, 2001.
  17. J. Watrous, The theory of quantum information. Cambridge university press, 2018.
  18. D. Aharonov, A. Kitaev, and N. Nisan, “Quantum circuits with mixed states,” in Proceedings of the thirtieth annual ACM symposium on Theory of computing, pp. 20–30, 1998.
  19. N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, “Bell nonlocality,” Reviews of modern physics, vol. 86, no. 2, p. 419, 2014.
  20. N. Jones and L. Masanes, “Interconversion of nonlocal correlations,” Physical Review A, p. 43–73, 2005.
  21. S. Pironio, J.-D. Bancal, and V. Scarani, “Extremal correlations of the tripartite no-signaling polytope,” Journal of Physics A: Mathematical and Theoretical, vol. 44, no. 6, p. 065303, 2011.
  22. D. Klyshko, “The Bell theorem and the problem of moments,” Physics Letters A, vol. 218, no. 3-6, pp. 119–127, 1996.
  23. J. J. Wallman and S. D. Bartlett, “Non-negative subtheories and quasiprobability representations of qubits,” Physical Review A, vol. 85, no. 6, p. 062121, 2012.
  24. M. J. Hoban, J. J. Wallman, and D. E. Browne, “Generalized Bell-inequality experiments and computation,” Physical Review A, vol. 84, no. 6, p. 062107, 2011.
  25. D. Avis and D. Bremner, “How good are convex hull algorithms?,” in Proceedings of the eleventh annual symposium on Computational geometry, pp. 20–28, 1995.
  26. M. Howard and E. Campbell, “Application of a resource theory for magic states to fault-tolerant quantum computing,” Physical review letters, vol. 118, no. 9, p. 090501, 2017.
  27. H. Pashayan, J. J. Wallman, and S. D. Bartlett, “Estimating outcome probabilities of quantum circuits using quasiprobabilities,” Physical review letters, vol. 115, no. 7, p. 070501, 2015.
  28. F. C. Peres, “Pauli-based model of quantum computation with higher-dimensional systems,” Physical Review A, vol. 108, no. 3, p. 032606, 2023.
  29. D. Zhou, B. Zeng, Z. Xu, and C. Sun, “Quantum computation based on d-level cluster state,” Physical Review A, vol. 68, no. 6, p. 062303, 2003.
  30. S. Bravyi, G. Smith, and J. A. Smolin, “Trading classical and quantum computational resources,” Physical Review X, vol. 6, no. 2, p. 021043, 2016.
  31. F. C. Peres and E. F. Galvão, “Quantum circuit compilation and hybrid computation using Pauli-based computation,” Quantum, vol. 7, p. 1126, 2023.
  32. V. Danos, E. Kashefi, and P. Panangaden, “The measurement calculus,” Journal of the ACM (JACM), vol. 54, no. 2, pp. 8–es, 2007.
  33. Cambridge university press Cambridge, 2001.
  34. M. Yoganathan, R. Jozsa, and S. Strelchuk, “Quantum advantage of unitary Clifford circuits with magic state inputs,” Proceedings of the Royal Society A, vol. 475, no. 2225, p. 20180427, 2019.
  35. M. Van den Nest, J. Dehaene, and B. De Moor, “Graphical description of the action of local Clifford transformations on graph states,” Physical Review A, vol. 69, no. 2, p. 022316, 2004.
  36. M. Hein, W. Dür, J. Eisert, R. Raussendorf, M. Nest, and H.-J. Briegel, “Entanglement in graph states and its applications,” arXiv preprint quant-ph/0602096, 2006.
  37. J. Barrett, “Information processing in generalized probabilistic theories,” Physical Review A, vol. 75, no. 3, p. 032304, 2007.
  38. M. Plávala, “General probabilistic theories: An introduction,” Physics Reports, vol. 1033, pp. 1–64, 2023.

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