Quantum Dynamics Simulation with Classical Oscillators

TL;DR

This paper explores how classical oscillators can simulate quantum dynamics, including entanglement, quantum gates, Landau-Zener transitions, and Fano resonances, providing a tangible classical analogy for quantum phenomena.

Contribution

It demonstrates the extent to which classical oscillators can replicate quantum properties and specific quantum phenomena, extending previous mappings to include entanglement and quantum gate operations.

Findings

Classical oscillators can simulate quantum entanglement and qubit manipulation.

Quantum phenomena like Landau-Zener transitions can be modeled with classical systems.

Classical models reproduce Fano resonances observed in quantum systems.

Abstract

In a previous paper [J.S.Briggs and A.Eisfeld, Phys.Rev.A 85, 052111] we showed that the time-development of the complex amplitudes of N coupled quantum states can be mapped by the time development of positions and velocities of N coupled classical oscillators. Here we examine to what extent this mapping can be realised to simulate the "quantum" properties of entanglement and qubit manipulation. By working through specific examples, e.g. of quantum gate operation, we seek to illuminate quantum/classical differences which hitherto have been treated more mathematically. In addition we show that important quantum coupled phenomena, such as the Landau-Zener transition and the occurrence of Fano resonances can be simulated by classical oscillators.