Parity Quantum Optimization: Compiler
Kilian Ender, Roeland ter Hoeven, Benjamin E. Niehoff, Maike Drieb-Schön, Wolfgang Lechner
Abstract
We introduce parity quantum optimization with the aim of solving optimization problems consisting of arbitrary <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi></mml:math>-body interactions and side conditions using planar quantum chip architectures. The method introduces a decomposition of the problem graph with arbitrary <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>k</mml:mi></mml:math>-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.