Parity Quantum Optimization: Encoding Constraints

TL;DR

This paper introduces a parity mapping method for quantum optimization that efficiently encodes constraints using parity variables, reducing overhead and enabling complex constraint implementation on 2D quantum systems.

Contribution

The paper presents a novel parity encoding approach that simplifies constraint implementation in quantum optimization problems without extra overhead.

Findings

Parity mapping encodes constraints with fewer qubits.

Constraints on k-body terms are implementable without overhead.

Method is suitable for 2D quantum systems.

Abstract

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.