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.

翻译：量子电路变换（QCT，又称量子比特映射）是量子电路编译中的关键步骤。通常，QCT通过寻找合适的初始映射并插入SWAP门来路由量子比特，以满足所有连通性约束。QCT的目标可以是最小化电路规模或深度。现有大多数QCT算法优先考虑最小化电路规模，可能忽略单量子比特门对电路深度的影响。本文首先指出，单次SWAP门插入可能使电路深度翻倍，并提出一种简单有效的方法来考虑单量子比特门对电路深度的影响。该方法可与多种现有QCT算法结合，以优化电路深度。Qiskit SABRE算法已被广泛认为是同时优化电路规模和深度的最优算法。我们将所提方法嵌入SABRE中，验证了其有效性：例如，在Google Sycamore和MQTBench中117个真实量子电路上，该方法可将电路深度最高降低50%，平均降低27%。