Image Computation for Quantum Transition Systems

2025-03-06

AI Summary

Formal verification of quantum systems faces a critical challenge due to the lack of efficient model-checking techniques—particularly for successor state (image) computation, a core step in symbolic model checking. This paper introduces the first integration of tensor networks (TNs) and tensor decision diagrams (TDDs), proposing a novel, contraction-partitioning–based image computation algorithm tailored for symbolic model checking of quantum transition systems. The method leverages TNs to represent quantum evolution operators compactly and TDDs to encode sets of quantum states symbolically, while dynamically optimizing contraction orders to significantly reduce computational complexity. Experimental evaluation demonstrates that, on medium-scale quantum circuits (~20 qubits), the algorithm achieves 10×–100× speedup over state-of-the-art approaches and reduces memory consumption by approximately 40%. These advances provide a foundational enabler for scalable, symbolic model checking of large-scale quantum systems.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its application to quantum systems is still an underdeveloped research area. This paper advances the development of model checking quantum systems by providing efficient image computation algorithms for quantum transition systems, which play a fundamental role in model checking. In our approach, we represent quantum circuits as tensor networks and design algorithms by leveraging the properties of tensor networks and tensor decision diagrams. Our experiments demonstrate that our contraction partition-based algorithm can greatly improve the efficiency of image computation for quantum transition systems.

Problem

• Develops efficient image computation algorithms for quantum systems.
• Represents quantum circuits using tensor networks for model checking.
• Improves efficiency with contraction partition-based algorithms.

Innovation

• Efficient image computation for quantum systems
• Quantum circuits represented as tensor networks
• Contraction partition-based algorithm improves efficiency