Equivalence Checking of Dynamic Quantum Circuits

TL;DR

This paper introduces a formal framework for dynamic quantum circuits, defining their functionality and proposing algorithms for their equivalence checking, which is crucial for verifying complex quantum algorithms on near-term devices.

Contribution

It provides the first formal semantics for dynamic quantum circuits and develops decision diagram-based algorithms for their equivalence checking.

Findings

Algorithms efficiently verify dynamic quantum circuit equivalence.

Classical logic embedding does not significantly increase resource requirements.

The approach enables reliable verification of complex quantum algorithms.

Abstract

Despite the rapid development of quantum computing these years, state-of-the-art quantum devices still contain only a very limited number of qubits. One possible way to execute more realistic algorithms in near-term quantum devices is to employ dynamic quantum circuits, in which measurements can happen during the circuit and their outcomes are used to control other parts of the circuit. This technique can help to significantly reduce the resources required to achieve a given accuracy of a quantum algorithm. However, since this type of quantum circuits are more flexible, their verification is much more challenging. In this paper, we give a formal definition of dynamic quantum circuits and then propose to characterise their functionality in terms of ensembles of linear operators. Based on this novel semantics, two dynamic quantum circuits are equivalent if they have the same functionality. We further propose and implement two decision diagram-based algorithms for checking the equivalence of dynamic quantum circuits. Experiments show that embedding classical logic into conventional quantum circuits does not incur significant time and space burden.