Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Frontiers in Optics

Optical matrix multiplication as an analogue for quantum computing

Isaac M. Nape, Mwezi Koni, Hadrian Bezuidenhout, Andrew Forbes

Published Jan 1, 2024• 1 citation
Publisher

Abstract

We report a technique for executing quantum computing protocols that are inspired by photonic matrix multiplication and exploits the inherent tensor product structure of transverse spatial modes.
DOI
10.1364/fio.2024.jtu5a.9

Related papers

Laser beams offer simplified calculations for quantum computing

Alane Lim

Well-established optical computing methods can be used to execute vector-matrix algebra for quantum computing.

Scilight•Oct 30, 2024•0 citations

Emulating quantum computing with optical matrix multiplication

Mwezi Koni, Hadrian Bezuidenhout, Isaac M. Nape

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, 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.

arXiv:2407.14178•APL Photonics•Oct 1, 2024•7 citations

Photonic Implementation of Quantum Computation Algorithm Based on Spatial Coding

Naoya Tate, Yusuke Ogura, Jun Tanida

Optical Review•Sep 1, 2007•0 citations

Photonic Causal Tensor Processor (PCTP): Hardware Architecture, Non-Commutative Optical Logic, and Topological State Execution

Michal Mazgal

Linear optical computing has emerged as a promising paradigm to bypass the thermodynamic constraints of von Neumann architectures and the Landauer dissipation limit (Emin = kBT ln2). However, existing integrated photonic accelerators remain fundamentally Markovian: they are restricted to commutative matrix-vector multiplications that systematically erase computational history during state aggregation. Here, we present the hardware architecture and operational principles of the Photonic Causal Tensor Processor (PCTP). Grounded in Causal Quaternionic Field Theory (CQFT), the PCTP natively executes the non-commutative Causal Tensor Product (⊠) governed by a rigorous chronological index (τ). We demonstrate how the four algebraic components of the quaternion (qa, qi, qj, qk) are directly mapped onto physical, orthogonal degrees of freedom of coherent optical wavepackets: real amplitude and longitudinal carrier phase, polarization states on the Poincaré sphere, and transverse orbital angular momentum (OAM) modes. We provide the physical layout of non-reciprocal causal logic gates utilizing low-loss Silicon Nitride (Si3N4) waveguides, magneto-optic Bismuth Iron Garnet (BIG) Faraday isolators, and synthetic diamond nitrogen-vacancy (NV) phase latches. The proposed processor executes deterministic causal tensor algebra at the speed of light with near-zero thermodynamic entropy generation, establishing an empirical hardware framework for post-quantum computing.

•Sep 25, 2026•0 citations

Tripartite nonseparability in classical optics

W. F. Balthazar, C. E. R. Souza, D. P. Caetano +3 more

It is possible to prepare classical optical beams which cannot be characterized by a tensor product of vectors describing each of their degrees of freedom. Here we report the experimental creation of such a nonseparable, tripartite GHZ-like state of path, polarization, and transverse modes of a classical laser beam. We use a Mach-Zehnder interferometer with an additional mirror and other optical elements to perform measurements that violate Mermin's inequality. This demonstration of a classical optical analogue of tripartite entanglement paves the path to novel optical applications inspired by multipartite quantum information protocols.

arXiv:1511.02265•Optics Letters•Dec 13, 2016•68 citations

Complex light for simulating quantum computing algorithms using reconfigurable optical vector-matrix multiplication

Isaac M. Nape

Complex Light and Optical Forces•Mar 19, 2025•0 citations
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, 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.
Linear optical computing has emerged as a promising paradigm to bypass the thermodynamic constraints of von Neumann architectures and the Landauer dissipation limit (Emin = kBT ln2). However, existing integrated photonic accelerators remain fundamentally Markovian: they are restricted to commutative matrix-vector multiplications that systematically erase computational history during state aggregation. Here, we present the hardware architecture and operational principles of the Photonic Causal Tensor Processor (PCTP). Grounded in Causal Quaternionic Field Theory (CQFT), the PCTP natively executes the non-commutative Causal Tensor Product (⊠) governed by a rigorous chronological index (τ). We demonstrate how the four algebraic components of the quaternion (qa, qi, qj, qk) are directly mapped onto physical, orthogonal degrees of freedom of coherent optical wavepackets: real amplitude and longitudinal carrier phase, polarization states on the Poincaré sphere, and transverse orbital angular momentum (OAM) modes. We provide the physical layout of non-reciprocal causal logic gates utilizing low-loss Silicon Nitride (Si3N4) waveguides, magneto-optic Bismuth Iron Garnet (BIG) Faraday isolators, and synthetic diamond nitrogen-vacancy (NV) phase latches. The proposed processor executes deterministic causal tensor algebra at the speed of light with near-zero thermodynamic entropy generation, establishing an empirical hardware framework for post-quantum computing.
It is possible to prepare classical optical beams which cannot be characterized by a tensor product of vectors describing each of their degrees of freedom. Here we report the experimental creation of such a nonseparable, tripartite GHZ-like state of path, polarization, and transverse modes of a classical laser beam. We use a Mach-Zehnder interferometer with an additional mirror and other optical elements to perform measurements that violate Mermin's inequality. This demonstration of a classical optical analogue of tripartite entanglement paves the path to novel optical applications inspired by multipartite quantum information protocols.