Parity Quantum Optimization: Encoding Constraints

Maike Drieb-Schön1,2, Kilian Ender1,2, Younes Javanmard1, 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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Constraints make hard optimization problems even harder to solve on quantum devices because they are implemented with large energy penalties and additional qubit overhead. The parity mapping, which has been introduced as an alternative to the spin encoding, translates the problem to a representation using only parity variables that encodes products of spin variables. In combining exchange interaction and single spin flip terms in the parity representation, constraints on sums and products of arbitrary $k$-body terms can be implemented without additional overhead in two-dimensional quantum systems.

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