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Toward Separating QMA from QCMA with a Classical Oracle

Author Mark Zhandry

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ACM Subject Classification
  • Theory of computation → Quantum complexity theory
Keywords
  • Quantum
  • Oracle Separations
  • QMA
  • QCMA

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Abstract

QMA is the class of languages that can be decided by an efficient quantum verifier given a quantum witness, whereas QCMA is the class of such languages where the efficient quantum verifier only is given a classical witness. A challenging fundamental goal in quantum query complexity is to find a classical oracle separation for these classes. In this work, we offer a new approach towards proving such a separation that is qualitatively different than prior work, and show that our approach is sound assuming a natural statistical conjecture which may have other applications to quantum query complexity lower bounds.

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Mark Zhandry. Toward Separating QMA from QCMA with a Classical Oracle. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 95:1-95:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.95

Author Details

Mark Zhandry
  • NTT Research, Sunnyvale, CA, USA

References

  1. Scott Aaronson and Greg Kuperberg. Quantum versus classical proofs and advice. In Twenty-Second Annual IEEE Conference on Computational Complexity (CCC'07), pages 115-128, 2007. URL: https://doi.org/10.1109/CCC.2007.27.
  2. Dorit Aharonov and Tomer Naveh. Quantum NP - A survey, 2002. Google Scholar
  3. Shalev Ben-David and Srijita Kundu. Oracle separation of QMA and QCMA with bounded adaptivity, 2024. Google Scholar
  4. Charles H. Bennett, Ethan Bernstein, Gilles Brassard, and Umesh Vazirani. Strengths and weaknesses of quantum computing. SIAM J. Comput., 26(5):1510-1523, October 1997. URL: https://doi.org/10.1137/S0097539796300933.
  5. Bill Fefferman and Shelby Kimmel. Quantum vs. classical proofs and subset verification. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018), 2018. URL: https://doi.org/10.4230/LIPIcs.MFCS.2018.22.
  6. Yassine Hamoudi and Frédéric Magniez. Quantum time-space tradeoff for finding multiple collision pairs. ACM Trans. Comput. Theory, April 2023. URL: https://doi.org/10.1145/3589986.
  7. Xingjian Li, Qipeng Liu, Angelos Pelecanos, and Takashi Yamakawa. Classical vs quantum advice and proofs under classically-accessible oracle. In Venkatesan Guruswami, editor, ITCS 2024, volume 287, pages 72:1-72:19. LIPIcs, January / February 2024. URL: https://doi.org/10.4230/LIPIcs.ITCS.2024.72.
  8. Qipeng Liu. Non-uniformity and quantum advice in the quantum random oracle model. In Carmit Hazay and Martijn Stam, editors, EUROCRYPT 2023, Part I, volume 14004 of LNCS, pages 117-143. Springer, Cham, April 2023. URL: https://doi.org/10.1007/978-3-031-30545-0_5.
  9. Andrew Lutomirski. Component mixers and a hardness result for counterfeiting quantum money, 2011. Google Scholar
  10. Anand Natarajan and Chinmay Nirkhe. A distribution testing oracle separating qma and qcma. In Proceedings of the Conference on Proceedings of the 38th Computational Complexity Conference, CCC '23, Dagstuhl, DEU, 2023. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.CCC.2023.22.
  11. R. J. Serfling. Probability Inequalities for the Sum in Sampling without Replacement. The Annals of Statistics, 2(1):39-48, 1974. URL: https://doi.org/10.1214/aos/1176342611.
  12. Terry Tao. 254a, notes 1: Concentration of measure. https://terrytao.wordpress.com/2010/01/03/254a-notes-1-concentration-of-measure/, 2010.
  13. Takashi Yamakawa and Mark Zhandry. Verifiable quantum advantage without structure. In 63rd FOCS, pages 69-74. IEEE Computer Society Press, October / November 2022. URL: https://doi.org/10.1109/FOCS54457.2022.00014.
  14. Mark Zhandry. Secure identity-based encryption in the quantum random oracle model. In Reihaneh Safavi-Naini and Ran Canetti, editors, CRYPTO 2012, volume 7417 of LNCS, pages 758-775. Springer, Berlin, Heidelberg, August 2012. URL: https://doi.org/10.1007/978-3-642-32009-5_44.
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