Efficient synthesis of quantum circuits implementing clifford group operations

Quantum circuits established themselves as a promising emerging technology and, hence, attracted considerable attention in the domain of computer-aided design. As a result, many approaches for synthesis of corresponding netlists have been proposed in the last decade. However, as the design of quantum circuits faces serious obstacles caused by phenomena such as superposition, entanglement, and phase shifts, automatic synthesis still represents a significant challenge. In this paper, we propose an automatic synthesis approach for quantum circuits that implement Clifford Group operations. These circuits are essential for many quantum applications and cover core aspects of quantum functionality. The proposed approach exploits specific properties of the unitary transformation matrices that are associated to quantum operations. Furthermore, Quantum Multiple-Valued Decision Diagrams (QMDDs) are employed for an efficient representation of these matrices. Experimental results confirm that this enables a compact realization of the respective quantum functionality.