Schrodinger Equation As a General Optimization Algorithm

TL;DR

This paper demonstrates that the Schrödinger equation can be interpreted as a global optimization algorithm, which significantly outperforms classical local optimization methods on hard problems.

Contribution

It introduces a novel perspective by deriving the Schrödinger equation as a general optimization algorithm, providing a new approach to solving complex optimization problems.

Findings

The quantum-inspired algorithm outperforms classical local methods on hard problems.

It finds solutions in seconds compared to hours for traditional algorithms.

The approach is benchmarked against randomly generated challenging optimization tasks.

Abstract

One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the quantum state of a physical system. It has been found that the time-independent version of the equation can be derived from a general optimization algorithm. Instead of arguing for a new interpretation and possible deeper principle for quantum mechanics, this paper elaborates a few points of the equation as a general global optimization algorithm. Benchmarked against randomly generated hard optimization problems, this paper shows that the algorithm significantly outperformed a classic local optimization algorithm. The former found a solution in one second with a single trial better than the best one found by the latter around one hour after one hundred thousand trials.