Quantum-like product states constructed from classical networks

TL;DR

This paper demonstrates how classical oscillator networks can be designed to mimic quantum states by exhibiting superpositions of tensor product basis states, enabling quantum-like operations within a classical framework.

Contribution

It introduces a novel mapping between quantum product states and classical oscillator networks, enabling quantum-like behavior in classical systems.

Findings

Established a one-to-one map between quantum basis states and classical oscillator network eigenstates.

Showed how quantum-like gates can operate on classical networks to perform quantum-like transformations.

Proved the existence of this mapping based on Cartesian products of graphs representing oscillator layouts.

Abstract

Can complex classical systems be designed to exhibit superpositions of tensor products of basis states, thereby mimicking quantum states? We exhibit a one-to one map between the product basis of quantum states comprising an arbitrary number of qubits and the eigenstates of a construction comprising classical oscillator networks. Specifically, we prove the existence of this map based on Cartesian products of graphs, where the graphs depict the layout of oscillator networks. We show how quantum-like gates can act on the classical networks to allow quantum-like operations in the state space.