Global optimization of spin Hamiltonians with gain-dissipative systems

TL;DR

This paper introduces a new class of gain-dissipative algorithms inspired by physical simulators to efficiently find the global minimum of complex spin Hamiltonians, outperforming classical algorithms in speed.

Contribution

The paper develops novel gain-dissipative algorithms for NP-hard problems, inspired by physical spin Hamiltonian simulators, demonstrating potential for significant speed-up over classical methods.

Findings

Potential for several orders of magnitude speed-up in large matrix problems

Performance comparison shows advantages over classical algorithms

Applicable to study ground states and statistical properties of spin systems

Abstract

Recently, several platforms were proposed and demonstrated a proof-of-principle for finding the global minimum of the spin Hamiltonians such as the Ising and XY models using gain-dissipative quantum and classical systems. The implementation of dynamical adjustment of the gain and coupling strengths has been established as a vital feedback mechanism for analog Hamiltonian physical systems that aim to simulate spin Hamiltonians. Based on the principle of operation of such simulators we develop a novel class of gain-dissipative algorithms for global optimisation of NP-hard problems and show its performance in comparison with the classical global optimisation algorithms. These systems can be used to study the ground state and statistical properties of spin systems and as a direct benchmark for the performance testing of the gain-dissipative physical simulators. The estimates of the time operation of the physical implementation of the gain-dissipative simulators for large matrices show a possible speed-up of the several orders of magnitude in comparison with classical computations.