Beating the efficiency of both quantum and classical simulations with semiclassics

TL;DR

This paper demonstrates that a specific semiclassical method can outperform both quantum and classical simulations in terms of speed and accuracy, especially in high-dimensional systems, challenging conventional expectations.

Contribution

It proves that the semiclassical dephasing representation can be both more accurate and faster than classical algorithms, with trajectory count independent of system dimensionality.

Findings

Semiclassical method requires a constant number of trajectories regardless of system size.

The method is faster than the most efficient classical algorithms.

Validated with simulations in systems up to 100 dimensions.

Abstract

While rigorous quantum dynamical simulations of many-body systems are extremely difficult (or impossible) due to the exponential scaling with dimensionality, corresponding classical simulations completely ignore quantum effects. Semiclassical methods are generally more efficient but less accurate than quantum methods, and more accurate but less efficient than classical methods. We find a remarkable exception to this rule by showing that a semiclassical method can be both more accurate and faster than a classical simulation. Specifically, we prove that for the semiclassical dephasing representation the number of trajectories needed to simulate quantum fidelity is independent of dimensionality and also that this semiclassical method is even faster than the most efficient corresponding classical algorithm. Analytical results are confirmed with simulations of quantum fidelity in up to 100 dimensions with 2^1700-dimensional Hilbert space.