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Quantum Delegation with an Off-The-Shelf Device

Authors Anne Broadbent, Arthur Mehta, Yuming Zhao

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Author Details

Anne Broadbent
  • Department of Mathematics and Statistics, University of Ottawa, Canada
  • Nexus for Quantum Technologies, University of Ottawa, Canada
Arthur Mehta
  • Department of Mathematics and Statistics, University of Ottawa, Canada
  • Nexus for Quantum Technologies, University of Ottawa, Canada
Yuming Zhao
  • Institute for Quantum Computing, University of Waterloo, Canada
  • Department of Pure Mathematics, University of Waterloo, Canada

Funding

This work was supported by the Mitacs Accelerate program IT24833 in collaboration with industry partner Agnostiq, online at https://agnostiq.ai.
  • Broadbent, Anne: A.B. is supported by the Air Force Office of Scientific Research under award number FA9550-20-1-0375, NSERC, and the University of Ottawa’s Research Chairs program.

Acknowledgements

We thank Seyed Sajjad Nezhadi, Gregory Rosenthal, William Slofstra, Jalex Stark, and Henry Yuen for discussions on the model. We thank Alex Grilo for discussions on some of our proof techniques. We also thank Thomas Vidick for detailed discussions on the formulation and proof of Theorem 19. We thank the anonymous reviewers for suggesting the use case of an OTS for a classical proof system.

Cite AsGet BibTex

Anne Broadbent, Arthur Mehta, and Yuming Zhao. Quantum Delegation with an Off-The-Shelf Device. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.TQC.2024.12

Abstract

Given that reliable cloud quantum computers are becoming closer to reality, the concept of delegation of quantum computations and its verifiability is of central interest. Many models have been proposed, each with specific strengths and weaknesses. Here, we put forth a new model where the client trusts only its classical processing, makes no computational assumptions, and interacts with a quantum server in a single round. In addition, during a set-up phase, the client specifies the size n of the computation and receives an untrusted, off-the-shelf (OTS) quantum device that is used to report the outcome of a single measurement. We show how to delegate polynomial-time quantum computations in the OTS model. This also yields an interactive proof system for all of QMA, which, furthermore, we show can be accomplished in statistical zero-knowledge. This provides the first relativistic (one-round), two-prover zero-knowledge proof system for QMA. As a proof approach, we provide a new self-test for n EPR pairs using only constant-sized Pauli measurements, and show how it provides a new avenue for the use of simulatable codes for local Hamiltonian verification. Along the way, we also provide an enhanced version of a well-known stability result due to Gowers and Hatami and show how it completes a common argument used in self-testing.

Subject Classification

ACM Subject Classification
  • Theory of computation → Interactive proof systems
  • Theory of computation → Quantum complexity theory
Keywords
  • Delegated quantum computation
  • zero-knowledge proofs
  • device-independence

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