published_or_final_version / abstract / toc / Physics / Master / Master of Philosophy

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Standard quantum computation proceeds via the unitary evolution of physical qubits (two-level 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. / Thesis (M.Sc.)-University of KwaZulu-Natal, Durban, 2011.

This thesis investigates several broad areas related to the effective implementation of quantum information processing, from large scale quantum algorithms and error correction, through to system identification and characterization techniques, efficient designs for quantum computing architectures and the design of small devices which utilize quantum effects. The discussion begins with the introduction of a quantum circuit appropriate for implementing Shor’s factoring algorithm on Linear Nearest Neighbor qubit arrays such as the Kane phosphorus in silicon system. Detailed numerical sim- ulations are then presented, demonstrating the sensitivity of the circuit under coherent quantum errors. The concepts of Quantum Error Correction and Fault-tolerant computation are reviewed with original work carried out to show the relative robustness and practicality of Fault-tolerant computation for logical state preparation. Methods of intrinsic system identification and characterization are proposed. Protocols for characterizing both the confinement of a multi-level system to the qubit subspace and the Hamiltonian dynamics governing two-qubit interactions are presented as well as a brief review of characterization techniques already developed for single qubit dynamics. (For complete abstract open document)

Thesis (M. Phil.)--University of Hong Kong, 2007. / Also available in print.

Thesis (BSc. (Hons))--Australian National University, 2002. / Available via the Australian National University Library Electronic Pre and Post Print Repository. Title from title screen (viewed Mar. 27, 2003). "November, 2002" "A thesis submitted in part fulfillment of the requirements for the degree of Bachelor of Science with Honours, from the Department of Physics, The Australian National University" Includes bibliographical references.

Thesis (Ph.D)--Physics, Georgia Institute of Technology, 2009. / Committee Chair: Chapman, Michael; Committee Member: Citrin, David; Committee Member: Kennedy, T. A. Brian; Committee Member: Kuzmich, Alexander; Committee Member: Raman, Chandra. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2008. / Minqiang Li, Committee Member ; Constantine Yannouleas, Committee Member ; Michael Pustilnik, Committee Member ; Mei-Yin Chou, Committee Member ; Uzi Landman, Committee Member.

A dissertation submitted in fulfillment of the requirements for the degree of Masters in Science in the, The Structured Light Group Department of Physics, University of the Witwatersrand, Johannesburg, 2018 / At the quantum level, entities and systems often behave counter-intuitively which we have come to describe with wave-particle duality. Accordingly, a particle that moves definitively from one position to another in our classical experience does something completely different on the quantum scale. The particle is not localized at any one position, but spreads out over all the possibilities as it moves. Here the particle can interfere with itself with wave-like propagation and generate, what is known as a Quantum Walk. This is the quantum mechanical analogue of the already well-known and used Random Walk where the particle takes random steps across the available positions, building up a series of random paths. The mechanics behind the random walk has already proved largely useful in many fields, from finance to simulation and computation. Analogously, the quantum walk promises even greater potential for development. Here, with many of the algorithms already developed, it would allow computations to outperform current classical methods on an unprecedented level. Additionally, by implementing these mechanics on various levels, it is possible to simulate and understand various quantum mechanical systems and phenomenon. This phenomenon consequently represents a significant advancement in several fields of study. Although there has been considerable theoretical development of this phenomenon, its potential now lies in implementing these quantum walks physically. Here, a physical system is required such that the quantum walk may be sustainably achieved, easily detected and dynamically altered as needed. Many systems have been subsequently proposed and demonstrated, but the criteria for a useful quantum walk leaves many such avenues lacking with the largest number of steps yet to reach 100 to the best of our knowledge. As a result, we explored a classical take on the quantum walk, utilizing the wave properties of light to achieve analogous mechanics with the advantage of the increased degree of control and robustness. While such an approach is not new, we considered a particular method where the quantum walk could be implemented in the spatial modes of light. By exploiting the non-separability (classical entanglement) of polarization and orbital angular momentum, such a classical quantum walk could be realized with greater intuitive implications and the potential for further study into the quantum mechanical nature of this phenomenon, over and above that of the other schemes, by walking the quantum-classical divide. The work presented here subsequently centres on experimentally achieving a quantum walk with classically entangled light for further development and useful implementation. Moreover, this work focused on demonstrating the sustainability, control and robustness necessary for this scheme to be beneficial for future development. In Chapter 1, an intuitive introduction is presented, highlighting the mechanics of this phenomenon that make it different from the Random walk counterpart. We also explore why this phenomenon is of such great importance with an overview of applications that physical implementation can result in. A more in-depth look into the dynamics and mathematical aspects of this walk is found in Chapter 2. Here a detailed look into the mechanisms behind the walk is taken with mathematical analysis. Furthermore, the subsequent differences and implications associated viii with utilizing classical light is explored, answering the question of what is quantum about the quantum walk. As the focus of this chapter is largely cemented in establishing a solid theoretical background, we also look into the physics behind classical light and develop the theoretical basis in the direction of structured light, with an emphasis on establishing classically entangled beams. Chapters 3 and 4 present the experimental work done throughout the course of this dissertation. With Chapter 3 we establish and characterize the elements necessary for obtaining a quantum walk in the spatial modes of light by utilizing waveplates as coins, q-plates as step operators and entanglement generators as well as mode sorters in a detection system. We also look into the characteristics of the modes that will be produced with these elements, allowing the propagation properties of the beam to be experimentally accounted for. In Chapter 4, we examine the experimental considerations of how to achieve a realistic and sustainable quantum walk. Here, we consider and implement the scheme proposed by Goyal et. al. [] where a light pulse follows a looped path, allowing the physical resources to be constant throughout the walk. We also show the experimental limitations of the equipment being utilized and the various steps needed to compensate. Finally, we not only implement a quantum walk with classically entangled light for the first time, but also demonstrate the flexibility of the system. Here, we achieve a maximum of 8 steps and show 5 different types of walks with varying dynamics and symmetry. The last chapter (Chapter 5) gives a summary of the dissertation in context of the goals and achievements of this work. The outlook and implications of these results are discussed and future steps outlined for extending this scheme into a highly competitive alternative for viable implementation of quantum walks for computing and simulation. / XL2019