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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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] 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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[8] 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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[11] Maike Drieb-Schön, Kilian Ender, Younes Javanmard, and Wolfgang Lechner, "Parity Quantum Optimization: Encoding Constraints", arXiv:2105.06235, (2021).

[12] Michael Fellner, Kilian Ender, Roeland ter Hoeven, and Wolfgang Lechner, "Parity Quantum Optimization: Benchmarks", arXiv:2105.06240, (2021).

[13] Krzysztof Domino, Akash Kundu, Özlem Salehi, and Krzysztof Krawiec, "Quadratic and higher-order unconstrained binary optimization of railway rescheduling for quantum computing", Quantum Information Processing 21 9, 337 (2022).

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

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

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[19] 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 2023-09-28 01:42:02) and SAO/NASA ADS (last updated successfully 2023-09-28 01:42:03). The list may be incomplete as not all publishers provide suitable and complete citation data.