Imitating quantum mechanics: qubit-based model for simulation

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.