Efficient Formal Verification of Quantum Error Correcting Programs

2025-04-10

AI Summary

This work addresses the low efficiency and insufficient trustworthiness of formal verification for quantum error correction (QEC) procedures. Methodologically: (1) We design a dedicated assertion logic and program logic, and fully formalize and mechanically verify their soundness in Coq; (2) We establish a differentiated verification condition (VC) solving framework—employing SMT solvers for automatic validity checking of Pauli errors, and introducing heuristic algorithms to enhance feasibility for non-Pauli errors; (3) We integrate the Coq proof assistant with an automated toolchain. Contributions include fully automated verification of 14 mainstream stabilizer codes across representative fault-tolerant scenarios—including gate-level fault tolerance, measurement noise, and circuit compilation—thereby significantly improving both verification efficiency and mathematical rigor. Veri-QEC provides a solid formal foundation for fault-tolerant quantum computation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Security and Privacy: Privacy-enhancing technologies
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

Abstract

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.

Problem

• Efficient verification of quantum error correcting programs
• Handling verification conditions for Pauli and non-Pauli errors
• Automated verifier for fault-tolerant quantum computation scenarios

Innovation

• Efficient verification framework for QEC programs
• Heuristic algorithm for non-Pauli errors
• Automated QEC verifier named Veri-QEC