Reduction of the energy-gap scaling by coherent catalysis in models of quantum annealing

TL;DR

This paper demonstrates through numerical analysis that coherent catalysis can reduce the energy gap scaling in quantum annealing models, potentially enabling exponential speedups even when non-stoquastic drivers are ineffective.

Contribution

It shows that coherent catalysis can induce polynomial energy gap scaling in models where non-stoquastic drivers fail, suggesting new avenues for quantum speedup.

Findings

Coherent catalysis leads to polynomial energy gap scaling in certain models.

Non-stoquastic drivers do not always change the phase transition order.

Potential for exponential speedups in previously hard quantum annealing problems.

Abstract

Non-stoquastic drivers are known to improve the performance of quantum annealing by reducing first-order phase transitions into second-order ones in several mean-field-type model systems. Nevertheless, statistical-mechanical analysis shows that some target Hamiltonians still exhibit unavoidable first-order transitions even with non-stoquastic drivers, making them difficult for quantum annealing to solve. Recently, a mechanism called coherent catalysis was proposed by Durkin [Phys. Rev. A \textbf{99}, 032315 (2019)], in which he showed the existence of a particular point on the line of first-order phase transitions where the energy gap scales polynomially as expected for a second-order transition. We show by extensive numerical computations that this phenomenon is observed in a few additional mean-field-type optimization problems where non-stoquastic drivers fail to change the order of phase transition in the thermodynamic limit. This opens up the possibility of using coherent catalysis to search for exponential speedups in systems previously thought to be exponentially slow for quantum annealing to solve.