Formal Verification of Abstract Interpreters for Quantum Circuits

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

Abstract interpreters are widely employed in quantum circuit simulation to provide efficient approximations of complex quantum states. However, ensuring the correctness of these abstractions—that is, guaranteeing the accuracy of the simulated quantum state—is a significant challenge. Traditional verification methods often struggle with the inherent complexity and probabilistic nature of quantum systems. This paper presents a novel formal verification framework that combines abstract interpretation, runtime monitoring, and probabilistic reasoning. The core idea is to build a layer of runtime monitoring that detects discrepancies between the abstract simulation and the underlying quantum circuit, leveraging probabilistic models to quantify the uncertainty introduced by the abstraction. This allows for a rigorous assessment of the simulation's accuracy, even for intricate quantum circuits. The framework provides a quantifiable measure of confidence in the simulation results, enabling developers to make informed decisions regarding the trade-off between accuracy and computational cost. We outline the key components of the framework, highlighting the integration of each technique and demonstrating its potential for enhancing the reliability of quantum circuit simulators.

DOI: 10.5281/zenodo.22441442

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