  Quantum annealing tends to be more difficult as the energy landscape of the
problem becomes complicated with many local minima. We have found a
transformation for changing the energy landscape that swaps the eigenvalues and
paired states without changing the eigenvalues of the instance at all. The
transformation is basically a partial recombination of the two-spin interaction
coefficient Jij and the longitudinal magnetic field interaction coefficient hi.
The Hamming distance corresponding to a barrier between the states changes by
the transformation, which in turn affects the ground state convergence. In the
quantum annealing simulation results of a small number of spin instances, the
annealing time was shortened by several orders of magnitude by applying the
transformation. In addition, we also obtained a result using a D-Wave quantum
annealer, which also showed a big improvement in the ground state convergence.
