QECV: Quantum Error Correction Verification

• URL: http://arxiv.org/abs/2111.13728v1
• Date: Fri, 26 Nov 2021 19:40:53 GMT
• Title: QECV: Quantum Error Correction Verification
• Authors: Anbang Wu, Gushu Li, Hezi Zhang, Gian Giacomo Guerreschi, Yuan Xie, Yufei Ding
• Abstract summary: We propose QECV, a verification framework that can efficiently verify the formal correctness of stabilizer codes. 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.
• Score: 15.05397810840915
• License: http://creativecommons.org/licenses/by/4.0/
• 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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