Equivalence Checking of Quantum Circuits via Path-Sum and Weighted Model Counting
This work provides a complete and efficient verification method for quantum circuit equivalence, addressing a key bottleneck in quantum computing compilation and optimization pipelines.
The paper introduces a hybrid method for equivalence checking of quantum circuits that combines path-sum reductions with a weighted model counting (WMC) encoding, achieving completeness beyond the Clifford fragment. The approach outperforms either component alone and competes with state-of-the-art tools on standard benchmarks.
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.