Partial Equivalence Checking of Quantum Circuits

TL;DR

This paper introduces a new method for checking partial equivalence between quantum circuits, enabling more flexible verification in quantum program compilation, which was previously limited by existing approaches.

Contribution

It provides a necessary and sufficient condition for partial equivalence and develops algorithms to verify this, enhancing quantum circuit optimization capabilities.

Findings

The method confirms the generality of partial equivalence checking.

Algorithms are efficient and effective in practical experiments.

Enables more aggressive optimization in quantum compilation.

Abstract

Equivalence checking of quantum circuits is an essential element in quantum program compilation, in which a quantum program can be synthesized into different quantum circuits that may vary in the number of qubits, initialization requirements, and output states. Verifying the equivalences among the implementation variants requires proper generality. Although different notions of quantum circuit equivalence have been defined, prior methods cannot check observational equivalence between two quantum circuits whose qubits are partially initialized, which is referred to as partial equivalence. In this work, we prove a necessary and sufficient condition for two circuits to be partially equivalent. Based on the condition, we devise algorithms for checking quantum circuits whose partial equivalence cannot be verified by prior approaches. Experiment results confirm the generality and demonstrate the efficiency and effectiveness of our method. Our result may unleash the optimization power of quantum program compilation to take more aggressive steps.