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.

@article{paperbot3066,
  title = {Efficient Formal Verification of Quantum Error Correcting Programs},
  author = {Qifan Huang and Li Zhou and Wang Fang and Mengyu Zhao and Mingsheng Ying},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {9},
  number = {PLDI},
  year = {2025},
  doi = {10.1145/3729293}
}