Cutting multi-control quantum gates with ZX calculus

Circuit cutting, the decomposition of a quantum circuit into independent partitions, has become a promising avenue towards experiments with larger quantum circuits in the noisy-intermediate scale quantum (NISQ) era. While previous work focused on cutting qubit wires or two-qubit gates, in this work we introduce a method for cutting multi-controlled Z gates. We construct a decomposition and prove the upper bound $\mathcal{O}(6^{2K})$ on the associated sampling overhead, where $K$ is the number of cuts in the circuit. This bound is independent of the number of control qubits but can be further reduced to $\mathcal{O}({4.5}^{2K})$ for the special case of CCZ gates. Furthermore, we evaluate our proposal on IBM hardware and experimentally show noise resilience due to the strong reduction of CNOT gates in the cut circuits.