We introduce an improved CNOT synthesis algorithm that considers nearest-neighbour interactions and CNOT gate error rates in noisy intermediate-scale quantum (NISQ) hardware. Compared to IBM's Qiskit compiler, it improves the fidelity of a synthesized CNOT circuit by about 2 times on average (up to 9 times). It lowers the synthesized CNOT count by a factor of 13 on average (up to a factor of 162). Our contribution is twofold. First, we define a $\textsf{Cost}$ function by approximating the average gate fidelity $F_{avg}$. According to the simulation results, $\textsf{Cost}$ fits the error probability of a noisy CNOT circuit, $\textsf{Prob} = 1 - F_{avg}$, much tighter than the commonly used cost functions. On IBM's fake Nairobi backend, it matches $\textsf{Prob}$ to within $10^{-3}$. On other backends, it fits $\textsf{Prob}$ to within $10^{-1}$. $\textsf{Cost}$ accurately quantifies the dynamic error characteristics and shows remarkable scalability. Second, we propose a noise-aware CNOT routing algorithm, NAPermRowCol, by adapting the leading Steiner-tree-based connectivity-aware CNOT synthesis algorithms. A weighted edge is used to encode a CNOT gate error rate and $\textsf{Cost}$-instructed heuristics are applied to each reduction step. NAPermRowCol does not use ancillary qubits and is not restricted to certain initial qubit maps. Compared with algorithms that are noise-agnostic, it improves the fidelity of a synthesized CNOT circuit across varied NISQ hardware. Depending on the benchmark circuit and the IBM backend selected, it lowers the synthesized CNOT count up to $56.95\%$ compared to ROWCOL and up to $21.62\%$ compared to PermRowCol. It reduces the synthesis $\textsf{Cost}$ up to $25.71\%$ compared to ROWCOL and up to $9.12\%$ compared to PermRowCol. Our method can be extended to route a more general quantum circuit, giving a powerful new tool for compiling on NISQ devices.

翻译：本文提出一种改进的CNOT综合算法，该算法综合考虑了噪声中等规模量子（NISQ）硬件中的最近邻相互作用与CNOT门错误率。与IBM的Qiskit编译器相比，该算法将综合后CNOT电路的保真度平均提升约2倍（最高可达9倍），并将综合CNOT门数量平均降低13倍（最高可达162倍）。我们的贡献主要体现在两个方面：首先，我们通过近似平均门保真度$F_{avg}$定义了$\textsf{Cost}$函数。仿真结果表明，相较于常用成本函数，$\textsf{Cost}$函数能更精确地拟合噪声CNOT电路的错误概率$\textsf{Prob} = 1 - F_{avg}$。在IBM的模拟Nairobi后端上，其与$\textsf{Prob}$的匹配误差在$10^{-3}$以内；在其他后端上，拟合误差在$10^{-1}$以内。$\textsf{Cost}$函数能准确量化动态错误特征，并展现出卓越的可扩展性。其次，我们通过改进当前主流的基于Steiner树的连通性感知CNOT综合算法，提出了噪声感知的CNOT布线算法NAPermRowCol。该算法采用加权边编码CNOT门错误率，并在每个归约步骤中应用$\textsf{Cost}$函数指导的启发式策略。NAPermRowCol无需使用辅助量子比特，且不受特定初始量子比特映射的限制。与噪声无关的算法相比，该算法能在不同NISQ硬件上显著提升综合CNOT电路的保真度。根据所选基准电路与IBM后端的不同，相较于ROWCOL算法，其可将综合CNOT门数量降低最高达$56.95\%$；相较于PermRowCol算法，最高可降低$21.62\%$。在综合$\textsf{Cost}$方面，较ROWCOL算法最高可减少$25.71\%$，较PermRowCol算法最高可减少$9.12\%$。本方法可进一步扩展至通用量子电路的布线问题，为NISQ设备上的编译任务提供强有力的新工具。