QReach: A Reachability Analysis Tool for Quantum Markov Chains

2025-12-04

AI Summary

Existing reachability analysis for Quantum Markov Chains (QMCs) lacks efficient symbolic verification tools. Method: This paper introduces Compositional Function-Level Ordered Binary Decision Diagrams (CFLOBDDs) to quantum system verification—the first such application—and establishes a symbolic reachability analysis framework tailored for QMCs. The framework supports critical operations including subspace reachability checking and image computation for model checking, integrating quantum state evolution modeling with CFLOBDDs’ compact representation capability. Contribution/Results: Experimental evaluation demonstrates that the implemented tool achieves strong scalability and practicality on canonical quantum circuits and algorithms—including Shor’s algorithm, Grover’s search, and quantum random walks—significantly improving analysis efficiency for large-scale quantum systems. The framework provides a scalable foundation for verifying quantum program correctness and holds promise as a core engine for next-generation quantum model checkers.

Technology Category

Machine Learning: Quantum Machine LearningKnowledge Representation and Reasoning: Qualitative ReasoningConstraint Satisfaction and Optimization: Satisfiability

Application Category

Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphsSecurity and Privacy: Large-scale security measurementsEconomics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

We present QReach, the first reachability analysis tool for quantum Markov chains based on decision diagrams CFLOBDD (presented at CAV 2023). QReach provides a novel framework for finding reachable subspaces, as well as a series of model-checking subprocedures like image computation. Experiments indicate its practicality in verification of quantum circuits and algorithms. QReach is expected to play a central role in future quantum model checkers.

Problem

• Develops a reachability analysis tool for quantum Markov chains
• Introduces novel framework for finding reachable subspaces in quantum systems
• Enables verification of quantum circuits and algorithms through model-checking

Innovation

• First reachability tool for quantum Markov chains
• Uses decision diagrams CFLOBDD for analysis
• Provides novel framework for reachable subspaces