Quantum error correction (QEC) is fundamental for suppressing noise in quantum hardware and enabling fault-tolerant quantum computation. In this paper, we propose an efficient verification framework for QEC programs. We define an assertion logic and a program logic specifically crafted for QEC programs and establish a sound proof system. We then develop an efficient method for handling verification conditions (VCs) of QEC programs: for Pauli errors, the VCs are reduced to classical assertions that can be solved by SMT solvers, and for non-Pauli errors, we provide a heuristic algorithm. We formalize the proposed program logic in Coq proof assistant, making it a verified QEC verifier. Additionally, we implement an automated QEC verifier, Veri-QEC, for verifying various fault-tolerant scenarios. We demonstrate the efficiency and broad functionality of the framework by performing different verification tasks across various scenarios. Finally, we present a benchmark of 14 verified stabilizer codes.

翻译：量子纠错（QEC）对于抑制量子硬件中的噪声和实现容错量子计算至关重要。本文提出了一种针对QEC程序的高效验证框架。我们专门为QEC程序定义了一种断言逻辑和一种程序逻辑，并建立了一个可靠性的证明系统。随后，我们开发了一种处理QEC程序验证条件（VC）的高效方法：对于泡利（Pauli）错误，验证条件被简化为可由SMT求解器解决的经典断言；对于非泡利错误，我们提供了一种启发式算法。我们在Coq证明助手中形式化了所提出的程序逻辑，使其成为一个经过验证的QEC验证器。此外，我们实现了一个自动化QEC验证器——Veri-QEC，用于验证各种容错场景。我们通过在不同场景下执行多种验证任务，展示了该框架的高效性和广泛的功能性。最后，我们提供了一个包含14个已验证稳定子码的基准测试集。