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On incorrectness logic for Quantum programs

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Nengkun YuAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 6, Issue OOPSLA1

Article No.: 72, Pages 1 - 28

https://doi.org/10.1145/3527316

Published: 29 April 2022 Publication History

Abstract

Bug-catching is important for developing quantum programs. Motivated by the incorrectness logic for classical programs, we propose an incorrectness logic towards a logical foundation for static bug-catching in quantum programming. The validity of formulas in this logic is dual to that of quantum Hoare logics. We justify the formulation of validity by an intuitive explanation from a reachability point of view and a comparison against several alternative formulations. Compared with existing works focusing on dynamic analysis, our logic provides sound and complete arguments. We further demonstrate the usefulness of the logic by reasoning several examples, including Grover's search, quantum teleportation, and a repeat-until-success program. We also automate the reasoning procedure by a prototyped static analyzer built on top of the logic rules.

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Cited By

Cousot PWang J(2025)Calculational Design of Hyperlogics by Abstract InterpretationProceedings of the ACM on Programming Languages10.1145/37048529:POPL(446-478)Online publication date: 7-Jan-2025
https://dl.acm.org/doi/10.1145/3704852
Cousot P(2024)Calculational Design of [In]Correctness Transformational Program Logics by Abstract InterpretationProceedings of the ACM on Programming Languages10.1145/36328498:POPL(175-208)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632849
(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

On incorrectness logic for Quantum programs
1. Computer systems organization
  1. Architectures
    1. Other architectures
      1. Quantum computing
2. Theory of computation
  1. Logic
    1. Programming logic

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 6, Issue OOPSLA1

April 2022

687 pages

EISSN:2475-1421

DOI:10.1145/3534679

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Copyright © 2022 Owner/Author.

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

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Association for Computing Machinery

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Publication History

Published: 29 April 2022

Published in PACMPL Volume 6, Issue OOPSLA1

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Cited By

Cousot PWang J(2025)Calculational Design of Hyperlogics by Abstract InterpretationProceedings of the ACM on Programming Languages10.1145/37048529:POPL(446-478)Online publication date: 7-Jan-2025
https://dl.acm.org/doi/10.1145/3704852
Cousot P(2024)Calculational Design of [In]Correctness Transformational Program Logics by Abstract InterpretationProceedings of the ACM on Programming Languages10.1145/36328498:POPL(175-208)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632849
(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)Analysis of quantum programsFoundations of Quantum Programming10.1016/B978-0-44-315942-8.00019-8(169-230)Online publication date: 2024
https://doi.org/10.1016/B978-0-44-315942-8.00019-8
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
Dwivedi KHaghparast MMikkonen T(2024)Quantum software engineering and quantum software development lifecycle: a surveyCluster Computing10.1007/s10586-024-04362-127:6(7127-7145)Online publication date: 1-Sep-2024
https://dl.acm.org/doi/10.1007/s10586-024-04362-1
Noll TGehnen CHermanns R(2024)Quantum Computing: From Weakest Preconditions to Voltage PulsesPrinciples of Verification: Cycling the Probabilistic Landscape10.1007/978-3-031-75783-9_9(201-229)Online publication date: 13-Nov-2024
https://doi.org/10.1007/978-3-031-75783-9_9
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
Chen YChung KLengál OLin JTsai WYen D(2023)An Automata-Based Framework for Verification and Bug Hunting in Quantum CircuitsProceedings of the ACM on Programming Languages10.1145/35912707:PLDI(1218-1243)Online publication date: 6-Jun-2023
https://dl.acm.org/doi/10.1145/3591270
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