Equivalence Checking of Quantum Circuits via Path-Sum and Weighted Model Counting

2026-04-27

AI Summary

This work addresses the problem of quantum circuit equivalence verification by proposing a hybrid method that integrates path-sum symbolic reduction with weighted model counting (WMC). The approach employs path-sum symbolic reduction whenever the circuits are reducible; otherwise, it invokes a WMC-based semantic decision procedure. Notably, this is the first integration of WMC into the path-sum framework, enabling complete equivalence verification for circuits containing non-Clifford gates and supporting semantic completeness up to global phase. Experimental results on standard benchmarks demonstrate that the proposed method significantly outperforms individual strategies and achieves state-of-the-art performance.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Equivalence checking of quantum circuits is a central verification task in quantum computing, ensuring the correctness of circuit optimizations, hardware mappings, and compilation pipelines. Among the primary symbolic methods for this purpose, the path-sum formalism provides a compact representation with powerful reduction rules that yield a canonical form for the classically simulable Clifford fragment, but confluence fails beyond the Clifford fragment. We introduce a new weighted model counting (WMC) encoding for path-sums and combine it with the existing path-sum reductions to obtain a verifier that is both complete and efficient. Our method applies reductions whenever possible and invokes the WMC-based decision procedure on the residual path-sum, yielding a complete semantic check up to a global phase. We implement the approach and evaluate it on standard benchmarks. Results show that the hybrid method outperforms either component in isolation and competes with state-of-the-art tools.

Problem

• equivalence checking
• quantum circuits
• verification
• path-sum
• weighted model counting

Innovation

• quantum circuit equivalence checking
• path-sum
• weighted model counting
• Clifford fragment
• hybrid verification