  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.
