Brief Announcement: Distributed Quantum Interactive Proofs

Authors François Le Gall, Masayuki Miyamoto, Harumichi Nishimura



PDF
Thumbnail PDF

File

LIPIcs.DISC.2022.48.pdf
  • Filesize: 448 kB
  • 3 pages

Document Identifiers

Author Details

François Le Gall
  • Graduate School of Mathematics, Nagoya University, Japan
Masayuki Miyamoto
  • Graduate School of Mathematics, Nagoya University, Japan
Harumichi Nishimura
  • Graduate School of Informatics, Nagoya University, Japan

Cite AsGet BibTex

François Le Gall, Masayuki Miyamoto, and Harumichi Nishimura. Brief Announcement: Distributed Quantum Interactive Proofs. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 48:1-48:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.DISC.2022.48

Abstract

The study of distributed interactive proofs was initiated by Kol, Oshman, and Saxena [PODC 2018] as a generalization of distributed decision mechanisms (proof-labeling schemes, etc.), and has received a lot of attention in recent years. In distributed interactive proofs, the nodes of an n-node network G can exchange short messages (called certificates) with a powerful prover. The goal is to decide if the input (including G itself) belongs to some language, with as few turns of interaction and as few bits exchanged between nodes and the prover as possible. There are several results showing that the size of certificates can be reduced drastically with a constant number of interactions compared to non-interactive distributed proofs. In this brief announcement, we introduce the quantum counterpart of distributed interactive proofs: certificates can now be quantum bits, and the nodes of the network can perform quantum computation. The main result of this paper shows that by using quantum distributed interactive proofs, the number of interactions can be significantly reduced. More precisely, our main result shows that for any constant k, the class of languages that can be decided by a k-turn classical (i.e., non-quantum) distributed interactive protocol with f(n)-bit certificate size is contained in the class of languages that can be decided by a 5-turn distributed quantum interactive protocol with O(f(n))-bit certificate size. We also show that if we allow to use shared randomness, the number of turns can be reduced to 3-turn. Since no similar turn-reduction classical technique is currently known, our result gives evidence of the power of quantum computation in the setting of distributed interactive proofs as well.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Quantum computation theory
Keywords
  • distributed interactive proofs
  • distributed verification
  • quantum computation

Metrics

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

References

  1. Pierluigi Crescenzi, Pierre Fraigniaud, and Ami Paz. Trade-Offs in Distributed Interactive Proofs. In Proceedings of the 33rd International Symposium on Distributed Computing (DISC 2019), pages 13:1-13:17, 2019. Google Scholar
  2. Pierre Fraigniaud, Amos Korman, and David Peleg. Local distributed decision. In Proceedings of the IEEE 52nd Annual Symposium on Foundations of Computer Science (FOCS 2011), pages 708-717, 2011. Google Scholar
  3. Mika Göös and Jukka Suomela. Locally checkable proofs in distributed computing. Theory of Computing, 12(1):1-33, 2016. Google Scholar
  4. Gillat Kol, Rotem Oshman, and Raghuvansh R Saxena. Interactive distributed proofs. In Proceedings of the 2018 ACM Symposium on Principles of Distributed Computing (PODC 2018), pages 255-264, 2018. Google Scholar
  5. Amos Korman, Shay Kutten, and David Peleg. Proof labeling schemes. Distributed Computing, 22(4):215-233, 2010. Google Scholar
  6. Moni Naor, Merav Parter, and Eylon Yogev. The power of distributed verifiers in interactive proofs. In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2020), pages 1096-115, 2020. Google Scholar
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