Imitating quantum mechanics: qubit-based model for simulation

TL;DR

This paper introduces a classical model that simulates quantum systems using harmonic functions to represent qubits, capturing key quantum phenomena like entanglement and enabling simulation of algorithms such as Shor's.

Contribution

It presents a novel classical approach to simulate quantum computation by representing qubits as harmonic functions, mimicking quantum tensor products and entanglement.

Findings

Successfully simulated Shor's algorithm

Demonstrated exponential growth in resource requirements with entanglement

Showed classical model can imitate quantum state space complexity

Abstract

We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations of different frequencies results in exponential growth of the state space similar to the tensor-product composition of qubit spaces in quantum mechanics. Individual qubits remain accessible in a composite system, which is represented as a complex function of a single variable, though entanglement imposes a demand on resources that scales exponentially with the number of entangled qubits. We carry out a simulation of Shor's algorithm and discuss a simpler implementation in this classical model.