Simple Glass Models and their Quantum Annealing

TL;DR

This paper analyzes first-order quantum phase transitions in mean-field spin glasses, demonstrating that the energy gap becomes exponentially small at the transition, which impacts the efficiency of quantum annealing.

Contribution

It provides an exact solution to the quantum Random Energy Model and introduces a two-time instanton method to estimate energy gaps in generic 'Random First Order' models.

Findings

Eigenstate projects onto unperturbed ground state at transition

Energy gap is exponentially small in system size

Implications for quantum annealing efficiency

Abstract

We study first order quantum phase transitions in mean-field spin glasses. We solve the quantum Random Energy Model using elementary methods and show that at the transition the eigenstate suddenly projects onto the unperturbed ground state and that the gap between the lowest states is exponentially small in the system size. We argue that this is a generic feature of all `Random First Order' models, which includes benchmarks such as random satisfiability. We introduce a two-time instanton to calculate this gap in general, and discuss the consequences for quantum annealing.