Equivalence Checking in Multi-level Quantum Systems

Motivated by its superiority compared to conventional solutions in many applications, quantum computation has intensely been investigated from a theoretical, physical, and design perspective. While these investigations mainly focused on two-level quantum systems, recently also advantages and benefits of higher-level quantum systems became evident. Though this led to several approaches for the representation and realization of quantum functionality in different dimensions, no efficient solution for verifying their equivalence has been proposed yet. In the present paper, we address this problem. We propose a scheme which is capable of verifying the equivalence of two quantum operations regardless of the dimension of their underlying quantum system. The proposed scheme can be incorporated into data-structures such as

Quantum Multiple-Valued Decision Diagrams

(QMDD) particularly suited for the representation of quantum functionality and, by this, enables an efficient verification. Experiments confirm the efficiency of the proposed approach.