Document Open Access Logo

Classical vs Quantum Advice and Proofs Under Classically-Accessible Oracle

Authors Xingjian Li , Qipeng Liu , Angelos Pelecanos , Takashi Yamakawa

PDF
Thumbnail PDF

File

LIPIcs.ITCS.2024.72.pdf
  • Filesize: 0.88 MB
  • 19 pages

Document Identifiers

Author Details

Xingjian Li
  • Tsinghua University, Beijing, China
Qipeng Liu
  • University of California at San Diego, La Jolla, CA, USA
Angelos Pelecanos
  • University of California at Berkeley, CA, USA
Takashi Yamakawa
  • NTT Social Informatics Laboratories, Tokyo, Japan

Funding

  • Liu, Qipeng: supported in part by the Simons Institute for the Theory of Computing, through a Quantum Postdoctoral Fellowship, by the DARPA SIEVE-VESPA grant No.HR00112020023 and by the NSF QLCI program through grant number OMA-2016245.
  • Pelecanos, Angelos: supported by DARPA under Agreement No. HR00112020023.

Cite AsGet BibTex

Xingjian Li, Qipeng Liu, Angelos Pelecanos, and Takashi Yamakawa. Classical vs Quantum Advice and Proofs Under Classically-Accessible Oracle. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 72:1-72:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.ITCS.2024.72

Abstract

It is a long-standing open question to construct a classical oracle relative to which BQP/qpoly ≠ BQP/poly or QMA ≠ QCMA. In this paper, we construct classically-accessible classical oracles relative to which BQP/qpoly ≠ BQP/poly and QMA ≠ QCMA. Here, classically-accessible classical oracles are oracles that can be accessed only classically even for quantum algorithms. Based on a similar technique, we also show an alternative proof for the separation of QMA and QCMA relative to a distributional quantumly-accessible classical oracle, which was recently shown by Natarajan and Nirkhe.

Subject Classification

ACM Subject Classification
  • Theory of computation → Complexity classes
  • Theory of computation → Quantum computation theory
Keywords
  • quantum computation
  • computational complexity

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Related Versions

References

  1. Scott Aaronson. Limitations of quantum advice and one-way communication. Theory Comput., 1(1):1-28, 2005. URL: https://doi.org/10.4086/toc.2005.v001a001.
  2. Scott Aaronson. The learnability of quantum states. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463(2088):3089-3114, September 2007. URL: https://doi.org/10.1098/rspa.2007.0113.
  3. Scott Aaronson, Harry Buhrman, and William Kretschmer. A qubit, a coin, and an advice string walk into a relational problem, 2023. URL: https://doi.org/10.48550/arXiv.2302.10332.
  4. Scott Aaronson and Andrew Drucker. A full characterization of quantum advice. SIAM J. Comput., 43(3):1131-1183, 2014. URL: https://doi.org/10.1137/110856939.
  5. 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. IEEE, 2007. Google Scholar
  6. Dorit Aharonov and Tomer Naveh. Quantum np - a survey. CoRR, 2002. URL: https://doi.org/10.48550/arXiv.quant-ph/0210077.
  7. Andris Ambainis, Leonard J. Schulman, Amnon Ta-Shma, Umesh V. Vazirani, and Avi Wigderson. The quantum communication complexity of sampling. SIAM J. Comput., 32(6):1570-1585, 2003. URL: https://doi.org/10.1137/S009753979935476.
  8. Ziv Bar-Yossef, T. S. Jayram, and Iordanis Kerenidis. Exponential separation of quantum and classical one-way communication complexity. In László Babai, editor, 36th ACM STOC, pages 128-137. ACM Press, June 2004. URL: https://doi.org/10.1145/1007352.1007379.
  9. Dan Boneh, Özgür Dagdelen, Marc Fischlin, Anja Lehmann, Christian Schaffner, and Mark Zhandry. Random oracles in a quantum world. In Dong Hoon Lee and Xiaoyun Wang, editors, ASIACRYPT 2011, volume 7073 of LNCS, pages 41-69. Springer, Heidelberg, December 2011. URL: https://doi.org/10.1007/978-3-642-25385-0_3.
  10. Harry Buhrman, Richard Cleve, and Avi Wigderson. Quantum vs. classical communication and computation. In Jeffrey Scott Vitter, editor, Proceedings of the Thirtieth Annual ACM Symposium on the Theory of Computing, Dallas, Texas, USA, May 23-26, 1998, pages 63-68. ACM, 1998. URL: https://doi.org/10.1145/276698.276713.
  11. Kai-Min Chung, Siyao Guo, Qipeng Liu, and Luowen Qian. Tight quantum time-space tradeoffs for function inversion. In 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS), pages 673-684. IEEE, 2020. Google Scholar
  12. Kai-Min Chung, Tai-Ning Liao, and Luowen Qian. Lower bounds for function inversion with quantum advice. arXiv preprint, 2019. URL: https://arxiv.org/abs/1911.09176.
  13. Sandro Coretti, Yevgeniy Dodis, Siyao Guo, and John P. Steinberger. Random oracles and non-uniformity. In Jesper Buus Nielsen and Vincent Rijmen, editors, EUROCRYPT 2018, Part I, volume 10820 of LNCS, pages 227-258. Springer, Heidelberg, April / May 2018. URL: https://doi.org/10.1007/978-3-319-78381-9_9.
  14. Anindya De, Luca Trevisan, and Madhur Tulsiani. Time space tradeoffs for attacks against one-way functions and PRGs. In Tal Rabin, editor, CRYPTO 2010, volume 6223 of LNCS, pages 649-665. Springer, Heidelberg, August 2010. URL: https://doi.org/10.1007/978-3-642-14623-7_35.
  15. Bill Fefferman and Shelby Kimmel. Quantum vs. classical proofs and subset verification. In Igor Potapov, Paul G. Spirakis, and James Worrell, editors, 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018, August 27-31, 2018, Liverpool, UK, volume 117 of LIPIcs, pages 22:1-22:23. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018. URL: https://doi.org/10.4230/LIPIcs.MFCS.2018.22.
  16. Dmitry Gavinsky. Classical interaction cannot replace a quantum message. In Proceedings of the fortieth annual ACM symposium on Theory of computing, pages 95-102, 2008. Google Scholar
  17. Siyao Guo, Qian Li, Qipeng Liu, and Jiapeng Zhang. Unifying presampling via concentration bounds. In Kobbi Nissim and Brent Waters, editors, TCC 2021, Part I, volume 13042 of LNCS, pages 177-208. Springer, Heidelberg, November 2021. URL: https://doi.org/10.1007/978-3-030-90459-3_7.
  18. Martin Hellman. A cryptanalytic time-memory trade-off. IEEE transactions on Information Theory, 26(4):401-406, 1980. Google Scholar
  19. Minki Hhan, Keita Xagawa, and Takashi Yamakawa. Quantum random oracle model with auxiliary input. In Advances in Cryptology-ASIACRYPT 2019: 25th International Conference on the Theory and Application of Cryptology and Information Security, Kobe, Japan, December 8-12, 2019, Proceedings, Part I, pages 584-614. Springer, 2019. Google Scholar
  20. Qipeng Liu. Non-uniformity and quantum advice in the quantum random oracle model. CoRR, 2022. URL: https://doi.org/10.48550/arXiv.2210.06693.
  21. Anand Natarajan and Chinmay Nirkhe. A classical oracle separation between qma and qcma. CoRR, 2022. URL: https://doi.org/10.48550/arXiv.2210.15380.
  22. Aran Nayebi, Scott Aaronson, Aleksandrs Belovs, and Luca Trevisan. Quantum lower bound for inverting a permutation with advice. arXiv preprint, 2014. URL: https://arxiv.org/abs/1408.3193.
  23. Harumichi Nishimura and Tomoyuki Yamakami. Polynomial time quantum computation with advice. Inf. Process. Lett., 90(4):195-204, 2004. URL: https://doi.org/10.1016/j.ipl.2004.02.005.
  24. Ran Raz. Exponential separation of quantum and classical communication complexity. In 31st ACM STOC, pages 358-367. ACM Press, May 1999. URL: https://doi.org/10.1145/301250.301343.
  25. Dominique Unruh. Random oracles and auxiliary input. In Alfred Menezes, editor, CRYPTO 2007, volume 4622 of LNCS, pages 205-223. Springer, Heidelberg, August 2007. URL: https://doi.org/10.1007/978-3-540-74143-5_12.
  26. Takashi Yamakawa and Mark Zhandry. Verifiable quantum advantage without structure. In 63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022, Denver, CO, USA, October 31 - November 3, 2022, pages 69-74. IEEE, 2022. URL: https://doi.org/10.1109/FOCS54457.2022.00014.
  27. Andrew Chi-Chih Yao. Coherent functions and program checkers (extended abstract). In 22nd ACM STOC, pages 84-94. ACM Press, May 1990. URL: https://doi.org/10.1145/100216.100226.
  28. Andrew Chi-Chih Yao. Quantum circuit complexity. In 34th FOCS, pages 352-361. IEEE Computer Society Press, November 1993. URL: https://doi.org/10.1109/SFCS.1993.366852.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact