Parity Quantum Optimization: Compiler

Kilian Ender1,2, Roeland ter Hoeven1,2, Benjamin E. Niehoff1, Maike Drieb-Schön1,2, and Wolfgang Lechner1,2

1Parity Quantum Computing GmbH, A-6020 Innsbruck, Austria
2Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria

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Abstract

We introduce parity quantum optimization with the aim of solving optimization problems consisting of arbitrary $k$-body interactions and side conditions using planar quantum chip architectures. The method introduces a decomposition of the problem graph with arbitrary $k$-body terms using generalized closed cycles of a hypergraph. Side conditions of the optimization problem in form of hard constraints can be included as open cycles containing the terms involved in the side conditions. The generalized parity mapping thus circumvents the need to translate optimization problems to a quadratic unconstrained binary optimization problem (QUBO) and allows for the direct encoding of higher-order constrained binary optimization problems (HCBO) on a square lattice and full parallelizability of gates.

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[3] Anette Messinger, Michael Fellner, and Wolfgang Lechner, 2023 IEEE International Conference on Quantum Computing and Engineering (QCE) 120 (2023) ISBN:979-8-3503-4323-6.

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[5] Roeland ter Hoeven, Anette Messinger, and Wolfgang Lechner, "Flexible constraint compilation in the parity architecture", Physical Review A 108 4, 042606 (2023).

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[7] Martin Lanthaler, Benjamin E. Niehoff, and Wolfgang Lechner, "Scalable set of reversible parity gates for integer factorization", Communications Physics 6 1, 73 (2023).

[8] Isaac D. Smith, Hendrik Poulsen Nautrup, and Hans J. Briegel, "Parity Quantum Computing as yz -Plane Measurement-Based Quantum Computing", Physical Review Letters 132 22, 220602 (2024).

[9] Dylan Herman, Cody Googin, Xiaoyuan Liu, Alexey Galda, Ilya Safro, Yue Sun, Marco Pistoia, and Yuri Alexeev, "A Survey of Quantum Computing for Finance", arXiv:2201.02773, (2022).

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[12] Clemens Dlaska, Kilian Ender, Glen Bigan Mbeng, Andreas Kruckenhauser, Wolfgang Lechner, and Rick van Bijnen, "Quantum Optimization via Four-Body Rydberg Gates", Physical Review Letters 128 12, 120503 (2022).

[13] Kilian Ender, Anette Messinger, Michael Fellner, Clemens Dlaska, and Wolfgang Lechner, "Modular Parity Quantum Approximate Optimization", PRX Quantum 3 3, 030304 (2022).

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[20] Maike Drieb-Schön, Kilian Ender, Younes Javanmard, and Wolfgang Lechner, "Parity Quantum Optimization: Encoding Constraints", arXiv:2105.06235, (2021).

[21] Michael Fellner, Anette Messinger, Kilian Ender, and Wolfgang Lechner, "Applications of universal parity quantum computation", Physical Review A 106 4, 042442 (2022).

[22] R. Cumming and T. Thomas, "Using a quantum computer to solve a real-world problem -- what can be achieved today?", arXiv:2211.13080, (2022).

[23] Michael Fellner, Kilian Ender, Roeland ter Hoeven, and Wolfgang Lechner, "Parity Quantum Optimization: Benchmarks", Quantum 7, 952 (2023).

[24] Maike Drieb-Schön, Kilian Ender, Younes Javanmard, and Wolfgang Lechner, "Parity Quantum Optimization: Encoding Constraints", Quantum 7, 951 (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-06-18 04:33:34) and SAO/NASA ADS (last updated successfully 2024-06-18 04:33:35). The list may be incomplete as not all publishers provide suitable and complete citation data.