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A Parameterized Framework for Quantum Computation

Mayfield, James L., IV

Abstract Details

2012, PhD, University of Cincinnati, Engineering and Applied Science: Computer Science and Engineering.

The primary focus of this dissertation is the development of a framework for the design and analysis of quantum circuits and quantum algorithms based on a parameterization of primitive quantum operators. Parameterized operators are characterized by the linear combination of two logically opposing operators. Single qubit operators can be viewed as a partial identification and negation. Similarly, conditional operators act partially in terms of a given condition and partially in terms of the logical negation of that condition. In support of this logic, several sets of basis operators are defined for n qubit computation and a hierarchy of these operators is established. A set of elementary n qubit operators is then placed within the general hierarchy of n qubit operators.

Within the framework, operators are further characterized by the encoding of binary information about their input to the phase of their output. This encoding is expressed as a boolean function on the n bit strings that correspond to the basis states of an n qubit state. Furthermore, interference between operators is characterized in terms of these encoding functions with specific relationships between the encoding functions producing a special case of interference dubbed decoding. When decoding occurs between two operators then the decoding operator effectively interprets the information encoded in the phase of a quantum state and produces a new state relative to the decoded information. The encoding and decoding properties of single qubit operators, elementary n qubit operators, and basic n qubit composite operators is developed. Finally, Deutsch's algorithm is analyzed and generalized by way of the parameterized operator and phase encoding/decoding framework.

Anca Ralescu, PhD (Committee Chair)
Kenneth Berman, PhD (Committee Member)
Marc Cahay, PhD (Committee Member)
Chia Han, PhD (Committee Member)
Dan Ralescu, PhD (Committee Member)
168 p.

Recommended Citations

Citations

  • Mayfield, IV, J. L. (2012). A Parameterized Framework for Quantum Computation [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1342543546

    APA Style (7th edition)

  • Mayfield, IV, James. A Parameterized Framework for Quantum Computation. 2012. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1342543546.

    MLA Style (8th edition)

  • Mayfield, IV, James. "A Parameterized Framework for Quantum Computation." Doctoral dissertation, University of Cincinnati, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1342543546

    Chicago Manual of Style (17th edition)