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Relational proofs for quantum programs

Authors:

Mingsheng Ying,

Li ZhouAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 4, Issue POPL

Article No.: 21, Pages 1 - 29

https://doi.org/10.1145/3371089

Published: 20 December 2019 Publication History

Abstract

Relational verification of quantum programs has many potential applications in quantum and post-quantum security and other domains. We propose a relational program logic for quantum programs. The interpretation of our logic is based on a quantum analogue of probabilistic couplings. We use our logic to verify non-trivial relational properties of quantum programs, including uniformity for samples generated by the quantum Bernoulli factory, reliability of quantum teleportation against noise (bit and phase flip), security of quantum one-time pad and equivalence of quantum walks.

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Cited By

Piattini MHevia JPeterssen G(2024)Quantum Software Engineering: Practical ChallengesInternational Journal of Software Engineering and Knowledge Engineering10.1142/S021819402441002X34:09(1387-1413)Online publication date: 30-Aug-2024
https://doi.org/10.1142/S021819402441002X
Yu N(2024)Quantum Temporal Logic and Reachability problems of Matrix SemigroupsInformation and Computation10.1016/j.ic.2024.105197(105197)Online publication date: Jul-2024
https://doi.org/10.1016/j.ic.2024.105197
(2024)ReferencesFoundations of Quantum Programming10.1016/B978-0-44-315942-8.00030-7(435-447)Online publication date: 2024
https://doi.org/10.1016/B978-0-44-315942-8.00030-7
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Index Terms

Relational proofs for quantum programs
1. Theory of computation

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 4, Issue POPL

January 2020

1984 pages

EISSN:2475-1421

DOI:10.1145/3377388

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Copyright © 2019 Owner/Author.

This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 20 December 2019

Published in PACMPL Volume 4, Issue POPL

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Cited By

Piattini MHevia JPeterssen G(2024)Quantum Software Engineering: Practical ChallengesInternational Journal of Software Engineering and Knowledge Engineering10.1142/S021819402441002X34:09(1387-1413)Online publication date: 30-Aug-2024
https://doi.org/10.1142/S021819402441002X
Yu N(2024)Quantum Temporal Logic and Reachability problems of Matrix SemigroupsInformation and Computation10.1016/j.ic.2024.105197(105197)Online publication date: Jul-2024
https://doi.org/10.1016/j.ic.2024.105197
(2024)ReferencesFoundations of Quantum Programming10.1016/B978-0-44-315942-8.00030-7(435-447)Online publication date: 2024
https://doi.org/10.1016/B978-0-44-315942-8.00030-7
Ying M(2024)Verification of quantum programsFoundations of Quantum Programming10.1016/B978-0-44-315942-8.00018-6(137-167)Online publication date: 2024
https://doi.org/10.1016/B978-0-44-315942-8.00018-6
Ying M(2024)Quantum Hoare logicFoundations of Quantum Programming10.1016/B978-0-44-315942-8.00016-2(91-134)Online publication date: 2024
https://doi.org/10.1016/B978-0-44-315942-8.00016-2
Ying M(2024)IntroductionFoundations of Quantum Programming10.1016/B978-0-44-315942-8.00009-5(1-9)Online publication date: 2024
https://doi.org/10.1016/B978-0-44-315942-8.00009-5
Yan PJiang HYu N(2024)Approximate Relational Reasoning for Quantum ProgramsComputer Aided Verification10.1007/978-3-031-65633-0_22(495-519)Online publication date: 24-Jul-2024
https://dl.acm.org/doi/10.1007/978-3-031-65633-0_22
Cruz-Lemus JRodríguez MBarba-Rojas RPiattini M(2024)Quantum Software Quality MetricsQuantum Software10.1007/978-3-031-64136-7_6(125-142)Online publication date: 23-Aug-2024
https://doi.org/10.1007/978-3-031-64136-7_6
Zhou LBarthe GStrub PLiu JYing M(2023)CoqQ: Foundational Verification of Quantum ProgramsProceedings of the ACM on Programming Languages10.1145/35712227:POPL(833-865)Online publication date: 9-Jan-2023
https://dl.acm.org/doi/10.1145/3571222
Deng YWu HXu M(2023)Local Reasoning About Probabilistic Behaviour for Classical–Quantum ProgramsVerification, Model Checking, and Abstract Interpretation10.1007/978-3-031-50521-8_8(163-184)Online publication date: 30-Dec-2023
https://doi.org/10.1007/978-3-031-50521-8_8
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