Simulation of quantum dynamics via classical collective behavior

TL;DR

This paper introduces a classical particle swarm algorithm to simulate non-relativistic quantum dynamics, capturing phenomena like entanglement and decoherence with linear computational complexity.

Contribution

The proposed method models quantum particles as swarms of classical samples with simple interactions, enabling efficient simulation of quantum phenomena including entanglement and Coulomb interactions.

Findings

Achieves square root speedup over traditional methods.

Successfully simulates Coulomb fields and quantum decoherence.

Includes natural generalization to quantum electrodynamics (QED).

Abstract

The simple algorithm for the simulation and visualization of non relativistic quantum dynamics is proposed that is based on a collective behavior of classical particles. Any quantum particle is represented as the swarm of its classical samples which interact by simple rules including emission and absorption of samples of tied photons. The quantum dynamics results from the collective behavior of such a swarm where the eigenstates are treated as the equilibrium states relatively to emission-absorption of photons. The entanglement is treated as a correlation between samples of the different swarms that is stored in the space-time part of the model inaccessible for a user. The amplitude is always grained. The Coulomb field between quantum particles is simulated, analogously to free flow of quantum package, by the point wise interaction between its samples and scalar photon samples which propagate by diffusion. It gives square root speedup in comparison to each-with-each method. This method obviously includes decoherence and admits the natural generalization on the QED of many particles with the linear computational cost.