Emulating quantum computing with optical matrix multiplication

TL;DR

This paper demonstrates how structured light can emulate quantum algorithms like Deutsch-Jozsa by using optical matrix multiplication, combining quantum principles with classical light to enhance optical computing capabilities.

Contribution

It introduces a method to perform quantum algorithm emulation using classical structured light and optical matrix multiplication, bridging quantum and classical optical computing.

Findings

Successful implementation of Deutsch-Jozsa algorithm with structured light

Use of Gaussian modes and spatial light modulators for reprogrammable optical computation

Establishment of a tensor product structure within light's degrees of freedom

Abstract

Optical computing harnesses the speed of light to perform vector-matrix operations efficiently. It leverages interference, a cornerstone of quantum computing algorithms, to enable parallel computations. In this work, we interweave quantum computing with classical structured light by formulating the process of photonic matrix multiplication using quantum mechanical principles such as state superposition and subsequently demonstrate a well known algorithm, namely the Deutsch-Jozsa's algorithm. This is accomplished by elucidating the inherent tensor product structure within the Cartesian transverse degrees of freedom of light, which is the main resource for optical vector-matrix multiplication. To this end, we establish a discrete basis using localized Gaussian modes arranged in a lattice formation and demonstrate the operation of a Hadamard Gate. Leveraging the reprogrammable and digital capabilities of spatial light modulators, coupled with Fourier transforms by lenses, our approach proves adaptable to various algorithms. Therefore our work advances the use of structured light for quantum information processing.