Quantum Circuit Equivalence Checking: A Tractable Bridge From Unitary to Hybrid Circuits

2025-11-27

AI Summary

Verifying equivalence of hybrid quantum circuits containing measurements remains challenging; existing approaches are largely restricted to purely unitary circuits or narrow subclasses, thus failing to support reliability assurance in practical quantum compilation toolchains. Method: We propose a general verification framework based on measurement delay: measurements are deferred to the circuit’s end, enabling unified treatment via separated projection operators, symbolic simulation, and unitary matrix representation, augmented with gate-level optimization strategies. Contribution/Results: This work is the first to systematically extend unitary-circuit equivalence techniques to broad classes of hybrid quantum circuits. The framework significantly improves both scalability and applicability, successfully validating equivalence in quantum teleportation, one-way quantum computation, and standard transformations in IBM Qiskit’s compiler. Moreover, it uncovers several previously undocumented equivalence anomalies within Qiskit’s compilation passes.

Technology Category

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

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Equivalence checking of hybrid quantum circuits is of primary importance, given that quantum circuit transformations are omnipresent along the quantum compiler chain. While some approaches exist for automating this task, most focus on the simple case of unitary circuits. At the same time, real quantum computing requires hybrid circuits equipped with measurement operators. Moreover, the few approaches targeting the hybrid case are limited to a restricted class of problems. We propose tackling the Quantum Hybrid Circuit Equivalence Checking problem through lifting unitary circuit verification using a transformation known as deferred measurement. We show that this approach alone significantly outperforms prior work, and that, with the addition of specific unitary-level techniques we call separation and projection, it can handle much larger classes of hybrid circuit equivalence problems. We have implemented and evaluated our method over standard circuit transformations such as teleportation, one-way measurement, or the IBM Qiskit compiler, demonstrating its promises. As a side finding, we have identified and reported several unexpected behaviours with the Qiskit compiler.

Problem

• Checking equivalence of hybrid quantum circuits with measurements
• Lifting unitary verification via deferred measurement transformation
• Handling larger classes of hybrid circuit equivalence problems

Innovation

• Lifting unitary verification via deferred measurement transformation
• Adding separation and projection techniques at unitary level
• Handling larger classes of hybrid circuit equivalence problems