Quantum probabilistic model checking

Abstract

Probabilistic Model Checking (PMC) is an automated method for analyzing probabilistic systems. For example, PMC is employed to verify the reliability of distributed systems, assess communication protocol performance, and evaluate the safety of autonomous driving systems, which are crucial for preventing human casualties. However, PMC struggles with the state explosion problem, which limits its scalability in complex and large systems. To address these issues, methods like statistical model checking have been proposed, but they still have limitations in analyzing large systems with high accuracy. In this thesis, we introduce Quantum Probabilistic Model Checking (QPMC), a new approach utilizing quantum computing to address the scalability-accuracy tradeoff in PMC. QPMC focuses on PMC problems associated with discrete-time Markov chains and bounded reachability. It efficiently translates large-scale PMC problems into quantum circuits, enabling quantum computers to solve PMC problems more efficiently. Additionally, QPMC proposes a technique for reducing the qubit requirements for practical resource limits. We prove the correctness of QPMC, ensuring that it correctly encodes PMC problems and produces results identical to traditional PMC. Our performance evaluation demonstrates that QPMC achieves a quadratic speedup compared to classical SMC. Experimentally, our qubit optimization technique has proven to reduce qubit usage by 15%-45% in select large-scale PMC problems.