Equivalence checking ofquantum circuits by nonlocality

Abstract

Suppose two quantum circuit chips are located at different places, for which we do not have any prior knowledge, and cannot see theinternal 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 thatexamines underlying quantum nonlocality, where the strongest nonlocality can be observed if and only if two quantum circuits are equivalentto each other. We show that the protocol also works approximately, where the distance between two quantumcircuits 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 discussthe possibility to generalize theprotocol to multipartite cases, i.e., if we do equivalence checking for multiple quantum circuits, we try to solve the problem in one go.