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.
 Andreas Wallraff, David I Schuster, Alexandre Blais, et al. ``Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics''. Nature 431, 162–167 (2004).
 L Childress, MV Gurudev Dutt, JM Taylor, et al. ``Coherent dynamics of coupled electron and nuclear spin qubits in diamond''. Science 314, 281–285 (2006).
 Xiaogang Qiang, Xiaoqi Zhou, Jianwei Wang, et al. ``Large-scale silicon quantum photonics implementing arbitrary two-qubit processing''. Nature photonics 12, 534–539 (2018).
 Philipp Hauke, Helmut G Katzgraber, Wolfgang Lechner, et al. ``Perspectives of quantum annealing: methods and implementations''. Reports on Progress in Physics 83, 054401 (2020).
 Rongxin Xia, Teng Bian, and Sabre Kais. ``Electronic structure calculations and the ising hamiltonian''. The Journal of Physical Chemistry B 122, 3384–3395 (2018).
 Alejandro Perdomo-Ortiz, Neil Dickson, Marshall Drew-Brook, et al. ``Finding low-energy conformations of lattice protein models by quantum annealing''. Scientific Reports 2, 571 (2012).
 Baonan Wang, Feng Hu, Haonan Yao, and Chao Wang. ``Prime factorization algorithm based on parameter optimization of ising model''. Scientific Reports 10, 7106 (2020).
 Wolfgang Lechner, Philipp Hauke, and Peter Zoller. ``A quantum annealing architecture with all-to-all connectivity from local interactions''. Science Advances 1 (2015).
 Nikolaj Moll, Panagiotis Barkoutsos, Lev S Bishop, et al. ``Quantum optimization using variational algorithms on near-term quantum devices''. Quantum Science and Technology 3, 030503 (2018).
 Martin Lanthaler, Clemens Dlaska, Kilian Ender, and Wolfgang Lechner, "Rydberg-Blockade-Based Parity Quantum Optimization", Physical Review Letters 130 22, 220601 (2023).
 Martin Lanthaler, Benjamin E. Niehoff, and Wolfgang Lechner, "Scalable set of reversible parity gates for integer factorization", Communications Physics 6 1, 73 (2023).
 Sheir Yarkoni, Elena Raponi, Thomas Bäck, and Sebastian Schmitt, "Quantum annealing for industry applications: introduction and review", Reports on Progress in Physics 85 10, 104001 (2022).
 Mohammadsadegh Khazali and Wolfgang Lechner, "Scalable quantum processors empowered by the Fermi scattering of Rydberg electrons", Communications Physics 6 1, 57 (2023).
 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).
 Dylan Herman, Ruslan Shaydulin, Yue Sun, Shouvanik Chakrabarti, Shaohan Hu, Pierre Minssen, Arthur Rattew, Romina Yalovetzky, and Marco Pistoia, "Constrained optimization via quantum Zeno dynamics", Communications Physics 6 1, 219 (2023).
 Kilian Ender, Anette Messinger, Michael Fellner, Clemens Dlaska, and Wolfgang Lechner, "Modular Parity Quantum Approximate Optimization", PRX Quantum 3 3, 030304 (2022).
 Federico Dominguez, Josua Unger, Matthias Traube, Barry Mant, Christian Ertler, and Wolfgang Lechner, "Encoding-Independent Optimization Problem Formulation for Quantum Computing", arXiv:2302.03711, (2023).
 Narendra N. Hegade, Koushik Paul, F. Albarrán-Arriagada, Xi Chen, and Enrique Solano, "Digitized adiabatic quantum factorization", Physical Review A 104 5, L050403 (2021).
 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).
 Michael Fellner, Anette Messinger, Kilian Ender, and Wolfgang Lechner, "Applications of universal parity quantum computation", Physical Review A 106 4, 042442 (2022).
 P. V. Sriluckshmy, Vicente Pina-Canelles, Mario Ponce, Manuel G. Algaba, Fedor Šimkovic, and Martin Leib, "Optimal, hardware native decomposition of parameterized multi-qubit Pauli gates", arXiv:2303.04498, (2023).
 Michael Fellner, Kilian Ender, Roeland ter Hoeven, and Wolfgang Lechner, "Parity Quantum Optimization: Benchmarks", Quantum 7, 952 (2023).
 Maike Drieb-Schön, Kilian Ender, Younes Javanmard, and Wolfgang Lechner, "Parity Quantum Optimization: Encoding Constraints", Quantum 7, 951 (2023).
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