Equivalence Checking of Parameterised Quantum Circuits

TL;DR

This paper introduces a new tensor decision diagram-based method for verifying the equivalence of parameterised quantum circuits, enabling efficient and direct comparison without parameter instantiation.

Contribution

It proposes a novel compact representation for PQCs and an algorithm for their equivalence checking that improves efficiency and effectiveness over existing methods.

Findings

The tensor decision diagram approach effectively verifies PQC equivalence.

Experimental results demonstrate the method's efficiency and accuracy.

The approach bridges the gap between theoretical models and practical quantum circuit implementations.

Abstract

Parameterised quantum circuits (PQCs) hold great promise for demonstrating quantum advantages in practical applications of quantum computation. Examples of successful applications include the variational quantum eigensolver, the quantum approximate optimisation algorithm, and quantum machine learning. However, before executing PQCs on real quantum devices, they undergo compilation and optimisation procedures. Given the inherent error-proneness of these processes, it becomes crucial to verify the equivalence between the original PQC and its compiled or optimised version. Unfortunately, most existing quantum circuit verifiers cannot directly handle parameterised quantum circuits; instead, they require parameter substitution to perform verification. In this paper, we address the critical challenge of equivalence checking for PQCs. We propose a novel compact representation for PQCs based on tensor decision diagrams. Leveraging this representation, we present an algorithm for verifying PQC equivalence without the need for instantiation. Our approach ensures both effectiveness and efficiency, as confirmed by experimental evaluations. The decision-diagram representations offer a powerful tool for analysing and verifying parameterised quantum circuits, bridging the gap between theoretical models and practical implementations.