Strong analog classical simulation of coherent quantum dynamics

TL;DR

This paper introduces a novel classical simulation scheme for quantum dynamics using geometric quantum mechanics and quantum tomography, capable of handling mixed states, nonunitary evolution, and infinite-dimensional systems.

Contribution

It presents a new strong analog classical simulation method that models quantum evolution as constrained classical Hamiltonian dynamics, expanding simulation capabilities.

Findings

Enables classical simulation of complex quantum systems.

Highlights the role of Hilbert space locality in simulation efficiency.

Provides examples demonstrating the method's effectiveness.

Abstract

A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational technique of quantum tomography, which applies broadly to cases of mixed states, nonunitary evolution, and infinite dimensional systems. The simulation provides an intriguing classical picture to probe quantum phenomena, namely, a coherent quantum dynamics can be viewed as a globally constrained classical Hamiltonian dynamics of a collection of coupled particles or strings. Efficiency analysis reveals a fundamental difference between the locality in real space and locality in Hilbert space, the latter enables efficient strong analog classical simulations. Examples are also studied to highlight the differences and gaps among various simulation methods.