Discrete optimization using quantum annealing on sparse Ising models

This paper discusses techniques for solving discrete optimization problems using quantumannealing. Practical issues likely to affect the computation include precision limitations, finitetemperature, bounded energy range, sparse connectivity, and small numbers of qubits. Toaddress these concerns we propose a way of finding energy representations with large classicalgaps between ground and first excited states, efficient algorithms for mapping non-compatibleIsing models into the hardware, and the use of decomposition methods for problems that aretoo large to fit in hardware. We validate the approach by describing experiments with D-Wavequantum hardware for low density parity check decoding with up to 1000 variables.