Equivalence checking of quantum circuits by nonlocality

TL;DR

This paper introduces a quantum nonlocality-based protocol for verifying the equivalence of two unknown quantum circuits, which is efficient, scalable, and applicable to multipartite cases.

Contribution

The authors develop a novel protocol that uses quantum nonlocality to determine circuit equivalence, with cost independent of circuit size and potential for generalization.

Findings

Protocol accurately detects exact circuit equivalence.

Approximate measures of circuit similarity are analytically derived.

Cost of the protocol is independent of circuit size.

Abstract

Suppose two quantum circuit chips are located at different places, for which we do not have any prior knowledge, and cannot see the internal structures either. If we want to find out whether they have the same functions or not with certainty, what should we do? In this paper, we show that this realistic problem can be solved completely from the viewpoints of quantum nonlocality. Specifically, we design an elegant protocol that examines underlying quantum nonlocality, where the strongest nonlocality can be observed if and only if two quantum circuits are equivalent to each other. We show that the protocol also works approximately, where the distance between two quantum circuits can be calculated accurately by observed quantum nonlocality in an analytical manner. Furthermore, it turns out that the computational cost of our protocol is independent in the size of compared quantum circuits. Lastly, we also discuss the possibility to generalize the protocol to multipartite cases, i.e., if we do equivalence checking for multiple quantum circuits, we try to solve the problem in one go.