A Novel Method of Function Extrapolation Inspired by Techniques in Low-entangled Many-body Physics

TL;DR

This paper presents a new function extrapolation method inspired by quantum mechanics, which maps function values onto quantum states and minimizes entanglement entropy to predict future values, showing improved performance on functions with sharp features.

Contribution

The paper introduces a quantum-inspired extrapolation algorithm that outperforms linear prediction for functions with complex features.

Findings

Comparable to linear prediction on simple functions

Better performance on functions with sharp features

Effective with noisy data

Abstract

We introduce a novel extrapolation algorithm inspired by quantum mechanics and evaluate its performance against linear prediction. Our method involves mapping function values onto a quantum state and estimating future function values by minimizing entanglement entropy. We demonstrate the effectiveness of our approach on various simple functions, both with and without noise, comparing it to linear prediction. Our results show that the proposed algorithm produces extrapolations comparable to linear prediction, while exhibiting improved performance for functions with sharp features.