  Circuit knitting is the process of partitioning large quantum circuits into
smaller subcircuits such that the result of the original circuits can be
deduced by only running the subcircuits. Such techniques will be crucial for
near-term and early fault-tolerant quantum computers, as the limited number of
qubits is likely to be a major bottleneck for demonstrating quantum advantage.
One typically distinguishes between gate cuts and wire cuts when partitioning a
circuit. The cost for any circuit knitting approach scales exponentially in the
number of cuts. One possibility to realize a cut is via the quasiprobability
simulation technique. In fact, we argue that all existing rigorous circuit
knitting techniques can be understood in this framework. Furthermore, we
characterize the optimal overhead for wire cuts where the subcircuits can
exchange classical information or not. We show that the optimal cost for
cutting $n$ wires without and with classical communication between the
subcircuits scales as $O(16^n)$ and $O(4^n)$, respectively.
