Portland State University. Department of Electrical and Computer Engineering
Term of Graduation
Date of Publication
Doctor of Philosophy (Ph.D.) in Electrical and Computer Engineering
Electrical and Computer Engineering
1 online resource (xv, 189 pages)
Quantum computing is a paradigm of computing using physical systems, which operate according to quantum mechanical principles. Since 2017, functioning quantum processing units with limited capabilities are available on the cloud. There are two models of quantum computing in the literature: discrete variable and continuous variable models. The discrete variable model is an extension of the binary logic of digital computing with quantum bits |0⟩ and |1⟩ . In the continuous variable model, the quantum state space is infinite-dimensional and the quantum state is expressed with an infinite number of basis elements.
In the physical implementation of quantum computing, however, the quantized energy levels of the electromagnetic field come in multiple values, naturally realizing the multi-valued logic of computing. Hence, to implement the discrete variable model (binary logic) of quantum computing, the temperature control is needed to restrict the energy levels to the lowest two to express the binary quantum states |0⟩ and |1⟩. The physical realization of the continuous variable model naturally implements the multi-valued logic of computing because any physical system always has the highest level of quantized energy observed i.e., the quantum state space is always finite dimensional.
In 2001, Knill, Laflamme, and Milburn proved that linear optics realizes universal quantum computing in the qubit-based model. Optical quantum computers by Xanadu, under the phase space representation of quantum optics, naturally realizes the multi-valued logic of quantum computing at room temperature. Optical quantum computers use optical signals, which are most compatible with the fiber optics communication network. They are easily fabricable for mass production, robust to noise, and have low latency.
Optical quantum computing provides flexibility to the users for determining the dimension of the computational space for each instance of computation. Additionally, nonlinear quantum optical effects are incorporated as nonlinear quantum gates. That flexibility of user-defined dimension of the computational space and availability of nonlinear gates lead to a faithful implementation of quantum neural networks in optical quantum computing. This dissertation provides a full description of a multi-class data quantum classifier on ten classes of the MNIST dataset.
In this dissertation, I provide the background information of optical quantum computing as an ideal candidate material for building the future classical-quantum hybrid internet for its numerous benefits, among which the compatibility with the existing communications/computing infrastructure is a main one. I also show that optical quantum computing can be a hardware platform for realizing the multi- valued logic of computing without the need to encode and decode computational problems in binary logic. I also derive explicit matrix representation of optical quantum gates in the phase space representation. Using the multi-valued logic of optical quantum computing, I introduce the first quantum multi-class data classifier, classifying all ten classes of the MNIST dataset.
©2023 Sophie Choe
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Choe, Sophie, "Realization of Multi-Valued Logic Using Optical Quantum Computing" (2023). Dissertations and Theses. Paper 6338.