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A verified optimizer for Quantum circuits

Authors:

Michael HicksAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 5, Issue POPL

Article No.: 37, Pages 1 - 29

https://doi.org/10.1145/3434318

Published: 04 January 2021 Publication History

Abstract

We present VOQC, the first fully verified optimizer for quantum circuits, written using the Coq proof assistant. Quantum circuits are expressed as programs in a simple, low-level language called SQIR, a simple quantum intermediate representation, which is deeply embedded in Coq. Optimizations and other transformations are expressed as Coq functions, which are proved correct with respect to a semantics of SQIR programs. SQIR uses a semantics of matrices of complex numbers, which is the standard for quantum computation, but treats matrices symbolically in order to reason about programs that use an arbitrary number of quantum bits. SQIR's careful design and our provided automation make it possible to write and verify a broad range of optimizations in VOQC, including full-circuit transformations from cutting-edge optimizers.

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Index Terms

A verified optimizer for Quantum circuits
1. Hardware
  1. Electronic design automation
    1. Logic synthesis
      1. Circuit optimization
  2. Emerging technologies
    1. Quantum technologies
      1. Quantum computation
2. Software and its engineering
  1. Software creation and management
    1. Software verification and validation
      1. Formal software verification

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 5, Issue POPL

January 2021

1789 pages

EISSN:2475-1421

DOI:10.1145/3445980

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Published: 04 January 2021

Published in PACMPL Volume 5, Issue POPL

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Cited By

Colledan ADal Lago U(2025)Flexible Type-Based Resource Estimation in Quantum Circuit Description LanguagesProceedings of the ACM on Programming Languages10.1145/37048839:POPL(1386-1416)Online publication date: 9-Jan-2025
https://dl.acm.org/doi/10.1145/3704883
Xu YBarthe GZhou L(2025)Automating Equational Proofs in Dirac NotationProceedings of the ACM on Programming Languages10.1145/37048789:POPL(1227-1259)Online publication date: 9-Jan-2025
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Amy MLunderville J(2025)Linear and Non-linear Relational Analyses for Quantum Program OptimizationProceedings of the ACM on Programming Languages10.1145/37048739:POPL(1072-1103)Online publication date: 9-Jan-2025
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Luo JZhao J(2025)Formalization of Quantum Intermediate Representations for code safetyJournal of Systems and Software10.1016/j.jss.2024.112236219:COnline publication date: 1-Jan-2025
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Shi ZChen G(2024)Formal Verification of Executable Matrix Inversion via Adjoint Matrix and Gaussian EliminationProceedings of the 26th International Symposium on Principles and Practice of Declarative Programming10.1145/3678232.3678242(1-13)Online publication date: 9-Sep-2024
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Huang KPalsberg J(2024)Compiling Conditional Quantum Gates without Using Helper QubitsProceedings of the ACM on Programming Languages10.1145/36564368:PLDI(1463-1484)Online publication date: 20-Jun-2024
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Yuan CCarbin M(2024)The T-Complexity Costs of Error Correction for Control Flow in Quantum ComputationProceedings of the ACM on Programming Languages10.1145/36563978:PLDI(492-517)Online publication date: 20-Jun-2024
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