Implementing Grover's search algorithm using the one-way quantum computing model and photonic orbital angular momentum.
Year: 2013
Type: dissertation
Abstract: Standard quantum computation proceeds via the unitary evolution of physical qubits (twolevel systems) that carry the information.A remarkably different model is one-way quantum computing where a quantum algorithm is implemented by a set of irreversible measurements on a large array of entangled qubits, known as the cluster state.The order and sequence of these measurements allow for different algorithms to be implemented.With a large enough cluster state and a method in which to perform single-qubit measurements the desired computation can be realised.We propose a potential implementation of one-way quantum computing using qubits encoded in the orbital angular momentum degree of freedom of single photons.Photons are good carriers of quantum information because of their weak interaction with the environment and the orbital angular momentum of single photons offers access to an infinite-dimensional Hilbert space for encoding information.Spontaneous parametric down-conversion is combined with a series of optical elements to generate a four-photon orbital angular momentum entangled cluster state and single-qubit measurements are carried out by means of digital holography.The proposed set-up, which is based on an experiment that utilised polarised photons, can be used to realise Grover's search algorithm which performs a search through an unstructured database of four elements.Our application is restricted to a two-dimensional subspace of a multi-dimensional system, but this research facilitates the use of orbital angular momentum qubits for quantum information processing and points towards the usage of photonic qudits (multi-level systems).We also review the application of Dirac notation to paraxial light beams on a classical and quantum level.This formalism is generally employed in quantum mechanics but the analogy with paraxial optics allows us to represent the classical states of light by means of Dirac kets.An analysis of the analogy between the classical and quantum states of light using this formalism, is presented.i Declaration 1 -Plagiarism I, Humairah Bassa declare that 1.The research reported in this dissertation, except where otherwise indicated, is my original research.2. This dissertation has not been submitted for any degree or examination at any other university.3. This dissertation does not contain other persons' data, pictures, graphs or other information, unless specifically acknowledged as being sourced from other persons.4. This dissertation does not contain other persons' writing, unless specifically acknowledged as being sourced from other researchers.Where other written sources have been quoted, then: a. Their words have been rewritten but the general information attributed to them has been referenced.
Author: Humairah Bassa
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1591642575