Circuit cutting via wire-cuts in ZX-calculus

Quantum circuit cutting refers to a series of techniques that allows one to partition a quantum computation on a large quantum computer into a quantum computation on smaller devices [1, 2, 3, 4]. This usually comes at the price of a sampling overhead, i.e., one needs to run the computation more times compared to the case without cutting. Additionally, these techniques rely on the possibility of finding decompositions of the ideal, global unitaries into quantum operations that can be implemented onto each sub-register, which ideally minimize the sampling overhead. In this work, we show how these decompositions can be obtained diagrammatically using ZX-calculus. The central idea of our work is that since in ZX-calculus only connectivity matters, it should be possible to cut wires in ZX-calculus by inserting known decompositions of the identity in standard quantum circuits. We show that using this basic idea many of the known decompositions known in the literature can be re-interpreted as an instance of wire-cuts in ZX calculus. We also obtain improved sampling overhead for multi-controlled Z gates [5]. Our work gives new ways of thinking about circuit cutting which can be particularly valuable for large unitaries.

[1] S. Bravyi, G. Smith & J. Smolin, Phys. Rev. X 6, 021043 (2016)

[2] T. Peng, A. Harrow, M. Ozols & X. Wu, Phys. Rev. Lett. 125, 150504 (2020)

[3] C. Piveteau & D. Sutter, IEEE Transactions on Information Theory 70, 4 (2023)

[4] K. Mitarai & K. Fujii, New Journal of Physics 23, 023021 (2021)

[5] C. Ufrecht, M. Periyasami, S. Rietsch, D. Scherer, A. Plinge & C. Mutschler, Quantum 7, 1147 (2023)