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Gleipnir: toward practical error analysis for Quantum programs

Authors:

Frederic T. Chong,

Ronghui GuAuthors Info & Claims

PLDI 2021: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation

Pages 48 - 64

https://doi.org/10.1145/3453483.3454029

Published: 18 June 2021 Publication History

Abstract

Practical error analysis is essential for the design, optimization, and evaluation of Noisy Intermediate-Scale Quantum(NISQ) computing. However, bounding errors in quantum programs is a grand challenge, because the effects of quantum errors depend on exponentially large quantum states. In this work, we present Gleipnir, a novel methodology toward practically computing verified error bounds in quantum programs. Gleipnir introduces the (ρ,δ)-diamond norm, an error metric constrained by a quantum predicate consisting of the approximate state ρ and its distance δ to the ideal state ρ. This predicate (ρ,δ) can be computed adaptively using tensor networks based on the Matrix Product States. Gleipnir features a lightweight logic for reasoning about error bounds in noisy quantum programs, based on the (ρ,δ)-diamond norm metric. Our experimental results show that Gleipnir is able to efficiently generate tight error bounds for real-world quantum programs with 10 to 100 qubits, and can be used to evaluate the error mitigation performance of quantum compiler transformations.

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Cited By

Pontolillo GMousavi M(2024)Delta Debugging for Property-Based Regression Testing of Quantum ProgramsProceedings of the 5th ACM/IEEE International Workshop on Quantum Software Engineering10.1145/3643667.3648219(1-8)Online publication date: 16-Apr-2024
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Tan SXiang DLu LLu JJiang QChen MYin JTsafrir DMusuvathi MGupta RAbu-Ghazaleh N(2024)MorphQPV: Exploiting Isomorphism in Quantum Programs to Facilitate Confident VerificationProceedings of the 29th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 310.1145/3620666.3651360(671-688)Online publication date: 27-Apr-2024
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Deng HPeng YHicks MWu X(2023)Automating NISQ Application Design with Meta Quantum Circuits with Constraints (MQCC)ACM Transactions on Quantum Computing10.1145/35793694:3(1-29)Online publication date: 8-Apr-2023
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Index Terms

Gleipnir: toward practical error analysis for Quantum programs
1. Theory of computation
  1. Models of computation
    1. Quantum computation theory
      1. Quantum information theory
  2. Semantics and reasoning
    1. Program reasoning
      1. Program analysis

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PLDI 2021: Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation

June 2021

1341 pages

ISBN:9781450383912

DOI:10.1145/3453483

General Chair:
Stephen N. Freund
Williams College, USA
,
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Eran Yahav
Technion, Israel

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Pontolillo GMousavi M(2024)Delta Debugging for Property-Based Regression Testing of Quantum ProgramsProceedings of the 5th ACM/IEEE International Workshop on Quantum Software Engineering10.1145/3643667.3648219(1-8)Online publication date: 16-Apr-2024
https://dl.acm.org/doi/10.1145/3643667.3648219
Tan SXiang DLu LLu JJiang QChen MYin JTsafrir DMusuvathi MGupta RAbu-Ghazaleh N(2024)MorphQPV: Exploiting Isomorphism in Quantum Programs to Facilitate Confident VerificationProceedings of the 29th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 310.1145/3620666.3651360(671-688)Online publication date: 27-Apr-2024
https://dl.acm.org/doi/10.1145/3620666.3651360
Deng HPeng YHicks MWu X(2023)Automating NISQ Application Design with Meta Quantum Circuits with Constraints (MQCC)ACM Transactions on Quantum Computing10.1145/35793694:3(1-29)Online publication date: 8-Apr-2023
https://dl.acm.org/doi/10.1145/3579369
Paltenghi MPradel M(2022)Bugs in Quantum computing platforms: an empirical studyProceedings of the ACM on Programming Languages10.1145/35273306:OOPSLA1(1-27)Online publication date: 29-Apr-2022
https://dl.acm.org/doi/10.1145/3527330
Yan PJiang HYu N(2022)On incorrectness logic for Quantum programsProceedings of the ACM on Programming Languages10.1145/35273166:OOPSLA1(1-28)Online publication date: 29-Apr-2022
https://dl.acm.org/doi/10.1145/3527316
Yuan CMcNally CCarbin M(2022)Twist: sound reasoning for purity and entanglement in Quantum programsProceedings of the ACM on Programming Languages10.1145/34986916:POPL(1-32)Online publication date: 12-Jan-2022
https://dl.acm.org/doi/10.1145/3498691
Arias DSanz Bde la Puerta JPastor IBringas P(2021)A Repeated Mistake is a Choice: Considering Security Issues and Risks in Quantum Computing from Scratch14th International Conference on Computational Intelligence in Security for Information Systems and 12th International Conference on European Transnational Educational (CISIS 2021 and ICEUTE 2021)10.1007/978-3-030-87872-6_16(156-166)Online publication date: 22-Sep-2021
https://doi.org/10.1007/978-3-030-87872-6_16

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