Diagonal unitary operators are well known to be key building blocks of many quantum algorithms and quantum computing procedures, and thus resource-efficient quantum circuit implementations are in demand. Here we propose a constructive algorithm that can generate a quantum circuit over the primitive gate set {cnot, $R_Z$} for realizing any given diagonal unitary operator piece by piece. The theoretical analysis reveals that, for the general case, our generated circuit not only ensures the asymptotically optimal gate count, but also nearly halves the circuit depth compared with the previous Welch's method [New J. Phys. 16, 033040 (2014)]. Specifically, this substantial depth optimization originates from the use of a uniform circuit rewriting rule developed here. The performance of our circuit synthesis algorithm is further validated by numerical evaluations on two examples. First, we achieve a nearly 50% depth reduction over Welch's method for synthesizing random diagonal unitary operators with up to 16 qubits. Second, we achieve an average of 22.05% depth reduction for resynthesizing the diagonal part of the specific quantum approximate optimization algorithm (QAOA) circuits with up to 14 qubits.

• Received 7 October 2023
• Accepted 29 February 2024

DOI:https://doi.org/10.1103/PhysRevA.109.042601