Cutting multi-control quantum gates with ZX calculus

Christian Ufrecht, Maniraman Periyasamy, Sebastian Rietsch, Daniel D. Scherer, Axel Plinge, and Christopher Mutschler

Fraunhofer IIS, Fraunhofer Institute for Integrated Circuits IIS, Division Positioning and Networks, Nuremberg, Germany

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Abstract

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.

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Cited by

[1] Sebastian Brandhofer, Ilia Polian, and Kevin Krsulich, "Optimal Partitioning of Quantum Circuits Using Gate Cuts and Wire Cuts", IEEE Transactions on Quantum Engineering 5, 1 (2024).

[2] Philipp Seitz, Manuel Geiger, and Christian B. Mendl, ISC High Performance 2024 Research Paper Proceedings (39th International Conference) 1 (2024) ISBN:978-3-9826336-0-2.

[3] Sebastian Brandhofer, Ilia Polian, and Kevin Krsulich, "Optimal Partitioning of Quantum Circuits using Gate Cuts and Wire Cuts", arXiv:2308.09567, (2023).

[4] Philipp Seitz, Manuel Geiger, Christian Ufrecht, Axel Plinge, Christopher Mutschler, Daniel D. Scherer, and Christian B. Mendl, "SCIM MILQ: An HPC Quantum Scheduler", arXiv:2404.03512, (2024).

[5] Philipp Seitz, Manuel Geiger, and Christian B. Mendl, "Multithreaded parallelism for heterogeneous clusters of QPUs", arXiv:2311.17490, (2023).

[6] Tuomas Laakkonen, Konstantinos Meichanetzidis, and John van de Wetering, "Picturing Counting Reductions with the ZH-Calculus", arXiv:2304.02524, (2023).

[7] Ryo Nagai, Shu Kanno, Yuki Sato, and Naoki Yamamoto, "Quantum channel decomposition with preselection and postselection", Physical Review A 108 2, 022615 (2023).

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