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 (two-level \nsystems) that carry the information. A remarkably different model is one-way quantum \ncomputing where a quantum algorithm is implemented by a set of irreversible measurements \non a large array of entangled qubits,, known as the cluster state. The order and sequence of \nthese measurements allow for different algorithms to be implemented. With a large enough \ncluster state and a method in which to perform single-qubit measurements the desired computation \ncan be realised. \nWe propose a potential implementation of one-way quantum computing using qubits encoded \nin the orbital angular momentum degree of freedom of single photons. Photons are good carriers \nof quantum information because of their weak interaction with the environment and the \norbital angular momentum of single photons offers access to an infinite-dimensional Hilbert \nspace for encoding information. Spontaneous parametric down-conversion is combined with \na series of optical elements to generate a four-photon orbital angular momentum entangled \ncluster state and single-qubit measurements are carried out by means of digital holography. \nThe proposed set-up, which is based on an experiment that utilised polarised photons, can be \nused to realise Grover’s search algorithm which performs a search through an unstructured \ndatabase of four elements. Our application is restricted to a two-dimensional subspace of a \nmulti-dimensional system, but this research facilitates the use of orbital angular momentum \nqubits for quantum information processing and points towards the usage of photonic qudits \n(multi-level systems). \nWe also review the application of Dirac notation to paraxial light beams on a classical and \nquantum level. This formalism is generally employed in quantum mechanics but the analogy \nwith paraxial optics allows us to represent the classical states of light by means of Dirac \nkets. An analysis of the analogy between the classical and quantum states of light using this \nformalism, is presented.
Author: Humairah Bassa
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1591642575