Shortcuts to Adiabatic Classical Spin Dynamics Mimicking Quantum Annealing

TL;DR

This paper introduces a simple method to create shortcuts to adiabaticity in classical spin systems, enabling efficient tracking of stationary states without prior knowledge, and applies it to mimic quantum annealing for optimization.

Contribution

The authors develop an easy-to-implement classical control scheme that mimics quantum annealing, bypassing complex calculations of counter-diabatic terms in many-body systems.

Findings

Control fields are constructed from state-dependent magnetic fields.

Method effectively mimics quantum annealing in classical spin systems.

Applicable to solving combinatorial optimization problems.

Abstract

We propose a simple construction of shortcuts to adiabaticity tracking instantaneous stationary states in classical spin systems without knowing tracked stationary states. In our construction, control fields of counter-diabatic driving are constituted by state-dependent magnetic fields, which can be easily determined with an aid of numerical calculations. Easiness of our construction is a remarkable feature since it is usually a hard task to determine explicit form of required counter-diabatic terms in many-body systems. We also argue that our method can be applied to solve combinatorial optimization problems by considering classical spin dynamics under a time-dependent Hamiltonian, which mimics the procedure of quantum annealing.