  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.
