  Commercial quantum annealers from D-Wave Systems make it possible to obtain
approximate solutions of high quality for certain NP-hard problems in nearly
constant time. Before solving a problem on D-Wave, several pre-processing
methods can be applied, one of them being the so-called spin reversal or gauge
transform. The spin reversal transform flips the sign of selected variables and
coefficients of the Ising or QUBO (quadratic unconstrained binary optimization)
representation of the problem that D-Wave minimizes. The spin reversal
transform leaves the ground state of the Ising model invariant, but can average
out the biases induced through analog and systematic errors on the device, thus
improving the quality of the solution that D-Wave returns. This work
investigates the effectiveness of the spin reversal transform for D-Wave 2000Q.
We consider two important NP-hard problems, the Maximum Clique and the Minimum
Vertex Cover problems, and show on a variety of input problem graphs that using
the spin reversal transform can yield substantial improvements in solution
quality. In contrast to the native spin reversal built into D-Wave, we consider
more general ways to reverse individual spins and we investigate the dependence
on the problem type, on the spin reversal probability, and possible advantages
of carrying out reversals on the qubit instead of the chain level. Most
importantly, for a given individual problem, we use our findings to optimize
the spin reversal transform using a genetic optimization algorithm.
