Emulating quantum computing with optical matrix multiplication
- URL: http://arxiv.org/abs/2407.14178v4
- Date: Thu, 10 Oct 2024 19:11:57 GMT
- Title: Emulating quantum computing with optical matrix multiplication
- Authors: Mwezi Koni, Hadrian Bezuidenhout, Isaac Nape,
- Abstract summary: Optical computing harnesses the speed of light to perform vector-matrix operations efficiently.
We formulate the process of photonic matrix multiplication using quantum mechanical principles.
We demonstrate a well known algorithm, namely the Deutsch-Jozsa's algorithm.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
Related papers
- A Photonic Parameter-shift Rule: Enabling Gradient Computation for Photonic Quantum Computers [0.0]
We present a method for gradient computation in quantum computation algorithms implemented on linear optical quantum computing platforms.
Our method scales linearly with the number of input photons and utilizes the same parameterized photonic circuit with shifted parameters for each evaluation.
arXiv Detail & Related papers (2024-10-03T17:47:38Z) - Evaluation of phase shifts for non-relativistic elastic scattering using quantum computers [39.58317527488534]
This work reports the development of an algorithm that makes it possible to obtain phase shifts for generic non-relativistic elastic scattering processes on a quantum computer.
arXiv Detail & Related papers (2024-07-04T21:11:05Z) - A Variational Approach to Learning Photonic Unitary Operators [0.0]
We harness the high dimensional nature of structured light modulated in the transverse spatial degree of freedom to learn unitary operations.
Our work advances high dimensional information processing and can be adapted to both process and quantum state tomography of unknown states and channels.
arXiv Detail & Related papers (2024-06-09T10:36:27Z) - A hybrid quantum-classical algorithm for multichannel quantum scattering
of atoms and molecules [62.997667081978825]
We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions.
The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix.
We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
arXiv Detail & Related papers (2023-04-12T18:10:47Z) - Quantum algorithms for matrix operations and linear systems of equations [65.62256987706128]
We propose quantum algorithms for matrix operations using the "Sender-Receiver" model.
These quantum protocols can be used as subroutines in other quantum schemes.
arXiv Detail & Related papers (2022-02-10T08:12:20Z) - Synthesis of Quantum Circuits with an Island Genetic Algorithm [44.99833362998488]
Given a unitary matrix that performs certain operation, obtaining the equivalent quantum circuit is a non-trivial task.
Three problems are explored: the coin for the quantum walker, the Toffoli gate and the Fredkin gate.
The algorithm proposed proved to be efficient in decomposition of quantum circuits, and as a generic approach, it is limited only by the available computational power.
arXiv Detail & Related papers (2021-06-06T13:15:25Z) - Quantum algorithms for powering stable Hermitian matrices [0.7734726150561088]
Matrix powering is a fundamental computational primitive in linear algebra.
We present two quantum algorithms that can achieve speedup over the classical matrix powering algorithms.
arXiv Detail & Related papers (2021-03-15T12:20:04Z) - Rapid characterisation of linear-optical networks via PhaseLift [51.03305009278831]
Integrated photonics offers great phase-stability and can rely on the large scale manufacturability provided by the semiconductor industry.
New devices, based on such optical circuits, hold the promise of faster and energy-efficient computations in machine learning applications.
We present a novel technique to reconstruct the transfer matrix of linear optical networks.
arXiv Detail & Related papers (2020-10-01T16:04:22Z) - Fast optimization of parametrized quantum optical circuits [0.0]
Parametrized quantum optical circuits are a class of quantum circuits in which the carriers of quantum information are photons and the gates are optical transformations.
We present an algorithm that is orders of magnitude faster than the current state of the art to compute the exact matrix elements of Gaussian operators and their gradient.
Our results will find applications in quantum optical hardware research, quantum machine learning, optical data processing, device discovery and device design.
arXiv Detail & Related papers (2020-04-23T07:02:45Z) - Programming a quantum computer with quantum instructions [39.994876450026865]
We use a density matrixiation protocol to execute quantum instructions on quantum data.
A fixed sequence of classically-defined gates performs an operation that uniquely depends on an auxiliary quantum instruction state.
The utilization of quantum instructions obviates the need for costly tomographic state reconstruction and recompilation.
arXiv Detail & Related papers (2020-01-23T22:43:29Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.