Energy landscape transformation of Ising problem with invariant eigenvalues for quantum annealing

TL;DR

This paper introduces a transformation that alters the energy landscape of Ising problems for quantum annealing, significantly improving convergence times by swapping eigenvalues and paired states without changing the eigenvalues.

Contribution

The authors propose a novel landscape transformation that modifies barrier heights and improves quantum annealing efficiency without altering the eigenvalues of the problem.

Findings

Annealing time was shortened by several orders of magnitude in simulations.

Transformation improved ground state convergence in D-Wave quantum annealer.

Landscape transformation affects barrier heights and state pairing without changing eigenvalues.

Abstract

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.