Quantum annealing speedup of embedded problems via suppression of Griffiths singularities

TL;DR

This paper demonstrates that optimizing embedding parameters in quantum annealing can suppress Griffiths singularities, significantly reducing annealing times and improving solution efficiency for embedded problems.

Contribution

It introduces a method to use embedding chains as a resource to alter the universality class of the problem, leading to faster quantum annealing.

Findings

Reduction of annealing time from exponential to polynomial in problem size

Numerical confirmation of improved time-to-solution with optimized embedding

Development of a custom integrator to enhance numerical convergence

Abstract

Optimal parameter setting for applications problems embedded into hardware graphs is key to practical quantum annealers (QA). Embedding chains typically crop up as harmful Griffiths phases, but can be used as a resource as we show here: to balance out singularities in the logical problem changing its universality class. Smart choice of embedding parameters reduces annealing times for random Ising chain from $O(exp[c\sqrt N])$ to $O(N^2)$. Dramatic reduction in time-to-solution for QA is confirmed by numerics, for which we developed a custom integrator to overcome convergence issues.