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arXiv · 2111.13728

QECV: Quantum Error Correction Verification

Anbang Wu·Gushu Li·Hezi Zhang·Gian Giacomo Guerreschi·Yuan Xie·Yufei Ding
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Abstract

Quantum Error Correction (QEC) is essential for fault-tolerant quantum copmutation, and its implementation is a very sophisticated process involving both quantum and classical hardware. Formulating and verifying the decomposition of logical operations into physical ones is a challenge in itself. In this paper, we propose QECV, a verification framework that can efficiently verify the formal correctness of stabilizer codes, arguably the most important class of QEC codes. QECV first comes with a concise language, QECV-Lang, where stabilizers are treated as a first-class object, to represent QEC programs. Stabilizers are also used as predicates in our new assertion language, QECV-Assn, as logical and arithmetic operations of stabilizers can be naturally defined. We derive a sound quantum Hoare logic proof system with a set of inference rules for QECV to efficiently reason about the correctness of QEC programs. We demonstrate the effectiveness of QECV with both theoretical complexity analysis and in-depth case studies of two well-known stabilizer QEC codes, the repetition code and the surface code.

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Anbang Wu, Gushu Li, Hezi Zhang, Gian Giacomo Guerreschi, Yuan Xie, Yufei Ding. 2021-11-26. QECV: Quantum Error Correction Verification. https://arxiv.org/abs/2111.13728

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