Upper bound inequality for calculation time in simulated annealing analogous to adiabatic theorem in quantum systems

TL;DR

This paper derives a classical analog to the quantum adiabatic theorem, establishing a practical lower bound on calculation time for simulated annealing that guarantees a certain accuracy level.

Contribution

It introduces an inequality for classical systems that relates calculation time and accuracy, inspired by quantum adiabatic principles, for improved simulated annealing performance.

Findings

Derived a classical speed limit inequality for simulated annealing

Established a trade-off relation between calculation time and accuracy

Provided a practical criterion for termination based on the inequality

Abstract

It has been recently reported that classical systems have speed limit for state evolution, although such a concept of speed limit had been considered to be unique to quantum systems. Owing to the speed limit for classical system, the lower bound for calculation time of simulated annealing with desired calculation accuracy can be derived. However, such a lower bound does not work as a criterion for completion of calculation in a practical time. In this paper, we derive an inequality for classical system analogous to the quantum adiabatic theorem that gives calculation time for an accuracy-guaranteed fluctuation-exploiting computation. The trade-off relation between calculation time and accuracy is given in the form tolerable in practical use.