Thermal, quantum and simulated quantum annealing: analytical comparisons for simple models

TL;DR

This paper compares classical, quantum, and simulated quantum annealing methods for simple models, analyzing their dynamics and differences in the thermodynamic limit using differential equations.

Contribution

It provides an analytical framework to describe and compare the behavior of various annealing techniques in simple mean-field models.

Findings

Quantum annealing follows Schrödinger evolution.

Simulated quantum annealing uses Quantum Monte Carlo dynamics.

Differences between quantum and simulated quantum annealing are characterized.

Abstract

We study various annealing dynamics, both classical and quantum, for simple mean-field models and explain how to describe their behavior in the thermodynamic limit in terms of differential equations. In particular we emphasize the differences between quantum annealing (i.e. evolution with Schr\"odinger equation) and simulated quantum annealing (i.e. annealing of a Quantum Monte Carlo simulation).