Approximate Quantum Circuit Synthesis for Diagonal Unitary

TL;DR

This paper introduces an efficient approximate quantum circuit synthesis algorithm for diagonal unitaries that reduces gate count and is capable of handling circuits up to 15 qubits within reasonable runtime.

Contribution

The paper presents a novel approximate synthesis algorithm for diagonal unitaries that optimizes quantum resource usage within specified error bounds, scalable to 15 qubits.

Findings

Achieves a 3.2ε reduction in CNOT gates on average within 0%-12% error range.

Synthesizes 12-qubit diagonal unitaries in about 6.57 seconds.

Synthesizes 15-qubit diagonal unitaries in approximately 561.71 seconds.

Abstract

The quantum circuit synthesis problem bridges quantum algorithm design and quantum hardware implementation in the Noisy Intermediate-Scale Quantum (NISQ) era. In quantum circuit synthesis problems, diagonal unitary synthesis plays a crucial role due to its fundamental and versatile nature. Meanwhile, experimental results have shown that moderately approximating the original algorithm to conserve quantum resources can improve the fidelity of algorithms during quantum execution. Building on this insight, we propose a quantum circuit synthesis algorithm to design diagonal unitary implementations based on specified quantum resource limits. Our algorithm can synthesize diagonal unitary for quantum circuits with up to 15 qubits on an ordinary laptop. In algorithm efficiency, synthesizing an n-qubit unitary matrix with an exact algorithm requires $2^n$ CNOT gates as a baseline. Within the algorithm error $\varepsilon $ range of interest (0\%-12\%), our algorithm achieves a $3.2\varepsilon $ reduction in CNOT gates on average. In runtime, the algorithm efficiently performs, synthesizing 12-qubit diagonal unitary in an average of 6.57 seconds and 15-qubit in approximately 561.71 seconds.