Please use this identifier to cite or link to this item: http://hdl.handle.net/10012/3316

 Title: Quantum Cellular Automata: Theory and Applications Authors: Perez Delgado, Carlos Antonio Keywords: Quantum ComputingCellular automata Approved Date: 26-Sep-2007 Date Submitted: 13-Sep-2007 Abstract: This thesis presents a model of Quantum Cellular Automata (QCA). The presented formalism is a natural quantization of the classical Cellular Automata (CA). It is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this model is to act as a theoretical model of quantum computation, similar to the quantum circuit model. The main advantage that QCA have over quantum circuits is that QCA make considerably fewer demands on the underlying hardware. In particular, as opposed to direct implementations of quantum circuits, the global evolution of the lattice in the QCA model does not assume independent control over individual \emph{qudits}. Rather, all qudits are to be addressed collectively in parallel. The QCA model is also shown to be an appropriate abstraction for space-homogeneous quantum phenomena, such as quantum lattice gases, spin chains and others. Some results that show the benefits of basing the model on local unitary operators are shown: computational universality, strong connections to the circuit model, simple implementation on quantum hardware, and a series of applications. A detailed discussion will be given on one particular application of QCA that lies outside either computation or simulation: single-spin measurement. This algorithm uses the techniques developed in this thesis to achieve a result normally considered hard in physics. It serves well as an example of why QCA are interesting in their own right. Program: Computer Science Department: School of Computer Science Degree: Doctor of Philosophy URI: http://hdl.handle.net/10012/3316 Appears in Collections: Electronic Theses and Dissertations (UW) Faculty of Mathematics Theses and Dissertations

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