Breaking the exponential wall in classical simulations of fidelity

TL;DR

This paper demonstrates that existing classical fidelity simulation algorithms generally scale exponentially with system size, but introduces a new algorithm with cost independent of dimensionality, offering a significant computational advantage.

Contribution

The paper presents a novel algorithm for classical fidelity simulation that maintains constant cost regardless of system size, unlike previous methods.

Findings

Existing algorithms scale exponentially with degrees of freedom.

The new algorithm has cost independent of system dimensionality.

An analytical approach to estimate efficiency of trajectory-based methods is proposed.

Abstract

We analyze the efficiency of available algorithms for the simulation of classical fidelity and show that their computational costs increase exponentially with the number of degrees of freedom for almost all initial states. Then we present an algorithm whose cost is independent of the system's dimensionality and show that, within a continuous family of algorithms, our algorithm is the only one with this property. Simultaneously we propose a general analytical approach to estimate efficiency of trajectory-based methods.