Quantum systems simulatability through classical networks

TL;DR

This paper establishes a theoretical framework connecting quantum systems via local transformations, enabling the simulation of complex quantum dynamics using classical circuits, which are easier to implement experimentally.

Contribution

It introduces a gauge group connecting quantum systems and extends classical circuit-based simulation methods to emulate quantum time evolution.

Findings

Quantum systems are equivalent under local transformations.

A gauge group links Hamiltonian operators of different quantum systems.

Classical circuits can simulate quantum time evolution via this framework.

Abstract

We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum system. Different quantum systems are connected in such way that studying one of them allows to understand the other. This result can be applied to the field of simulation of quantum systems, in order to mimic more complicated quantum systems from another simulatable quantum system. Given that there is a bridge that allows to simulate a particular quantum system on this kind of Hilbert spaces using classical circuits we will provide a general scenario to extend this bridge to simulate the time evolution, via Schr\"odinger equation, of any of these quantum system using classical circuits. This classical systems can be implemented and controlled more easily in the laboratory than the quantum systems.