A common approach to quantum circuit transformation is to use the properties of a specific gate set to create an efficient representation of a given circuit's unitary, such as a parity matrix or stabiliser tableau, and then resynthesise an improved circuit, e.g. with fewer gates or respecting connectivity constraints. Since these methods rely on a restricted gate set, generalisation to arbitrary circuits usually involves slicing the circuit into pieces that can be resynthesised and working with these separately. The choices made about what gates should go into each slice can have a major effect on the performance of the resynthesis. In this paper we propose an alternative approach to generalising these resynthesis algorithms to general quantum circuits. Instead of cutting the circuit into slices, we "cut out" the gates we can't resynthesise leaving holes in our quantum circuit. The result is a second-order process called a quantum comb, which can be resynthesised directly. We apply this idea to the RowCol algorithm, which resynthesises CNOT circuits for topologically constrained hardware, explaining how we were able to extend it to work for quantum combs. We then compare the generalisation of RowCol using our method to the naive "slice and build" method empirically on a variety of circuit sizes and hardware topologies. Finally, we outline how quantum combs could be used to help generalise other resynthesis algorithms.

翻译：将量子电路变换的一种常见方法是利用特定门集合的性质，为给定电路的酉算子（如奇偶校验矩阵或稳定子表格）创建高效表示，然后重新合成改进后的电路（例如减少门数或满足连通性约束）。由于这些方法依赖于受限门集合，将其推广到任意电路通常需要将电路分割成可重新合成的片段并分别处理。各片段中门的选择会对重合成性能产生重大影响。本文提出一种将重合成算法推广到通用量子电路的新方法：我们不切割电路片段，而是"挖掉"无法重合成的门，在量子电路中留下"孔洞"，从而得到一个称为量子梳的二阶过程，该过程可直接进行重合成。我们将此思想应用于RowCol算法——该算法针对拓扑约束硬件重合成CNOT电路，并阐述了如何将其扩展至处理量子梳。随后在多种电路规模和硬件拓扑结构下，通过实验将我们的方法推广的RowCol算法与朴素的"切片-构建"方法进行对比。最后，我们概述了量子梳如何助力其他重合成算法的推广。