Ultimate Limits to Computation: Anharmonic Oscillator

TL;DR

This paper investigates the fundamental speed limits of computation using an anharmonic oscillator, establishing upper bounds on orthogonalization time and analyzing complexity growth under perturbations.

Contribution

It introduces a novel analysis of the minimum orthogonalization time and complexity growth in anharmonic oscillators, revealing critical points affecting computational rate.

Findings

Derived an upper bound on the rate of orthogonalization.

Identified a critical point where complexity growth behavior changes.

Numerical analysis supports the existence of phase space critical points.

Abstract

Motivated by studies of ultimate speed of computers, we examine the question of minimum time of orthogonalization in a simple anharmonic oscillator and find an upper bound on the rate of computations. Furthermore, we investigate the growth rate of complexity of operation when the system undergoes a definite perturbation. At the phase space of the parameters, by numerical analysis, we find the critical point where beyond that the rate of complexity changes its behavior.