Parity Quantum Optimization: Encoding Constraints

Constraints make hard optimization prob-lems even more challenging to solve on quan-tum devices because they are typically imple-mented with large energy penalties and addi-tional qubit overhead. The parity mapping, which has been introduced as an alternative to the spin encoding, translates the problem to a representation using parity variables that encode products of spin variables into a single parity variable. By combining exchange inter-action and single spin flip terms in the parity representation, constraints on sums, products of arbitrary k-body terms and sums over such products can be implemented without penalty terms in two-dimensional quantum systems.