Single-Qubit Gates Matter for Optimising Quantum Circuit Depth in Qubit Mapping

TL;DR

This paper highlights the importance of single-qubit gates in quantum circuit mapping and introduces a method to optimize circuit depth by considering their impact, significantly improving existing algorithms like SABRE.

Contribution

It presents a novel approach that incorporates single-qubit gate effects into quantum circuit transformation, enhancing depth optimization in existing algorithms.

Findings

Reduced circuit depth by up to 50%

Achieved an average of 27% depth reduction

Effective integration with SABRE algorithm

Abstract

Quantum circuit transformation (QCT, a.k.a. qubit mapping) is a critical step in quantum circuit compilation. Typically, QCT is achieved by finding an appropriate initial mapping and using SWAP gates to route the qubits such that all connectivity constraints are satisfied. The objective of QCT can be to minimise circuit size or depth. Most existing QCT algorithms prioritise minimising circuit size, potentially overlooking the impact of single-qubit gates on circuit depth. In this paper, we first point out that a single SWAP gate insertion can double the circuit depth, and then propose a simple and effective method that takes into account the impact of single-qubit gates on circuit depth. Our method can be combined with many existing QCT algorithms to optimise circuit depth. The Qiskit SABRE algorithm has been widely accepted as the state-of-the-art algorithm for optimising both circuit size and depth. We demonstrate the effectiveness of our method by embedding it in SABRE, showing that it can reduce circuit depth by up to 50% and 27% on average on, for instance, Google Sycamore and 117 real quantum circuits from MQTBench.