A path dependent quantum approximate optimization algorithm optimized by pairwise correlation of angles

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Daniel, C. (2021). A path dependent quantum approximate optimization algorithm optimized by pairwise correlation of angles. Unc Charlotte Electronic Theses And Dissertations.
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Abstract

Given the current promise of quantum computing to increase the efficiency of optimization algorithms, it is important to utilize these quantum algorithms for useful applications. The quantum approximate optimization algorithm was recently developed to accommodate combinatorial optimization problems where the minimum of a cost function is required for an optimal solution. We consider appropriate cost Hamiltonians of the long-range spin glass Ising model with the objectives to solve for an unknown a priori ground state and an unknown sequence of unitary operators to move an initial Hadamard quantum state to an arbitrary eigenstate of the Hamiltonian. We utilize a path dependent quantum approximate optimization algorithm optimized by considering the pairwise correlation of angles on its path to the global optimum of the entire angle parameter space. An importance sampling technique is used to distribute the probability of selecting a specific pair of angles to optimize along its path as it evolves with the depth of the quantum circuit. We also simulate the measurement process classically to resemble the sample outputs of a quantum computer and to determine how the sampling affects the performance of this algorithm. Lastly, results are demonstrated to justify this new approach to the quantum approximate optimization algorithm as a viable technique to solve quantum computational optimization problems.

Details
Author

Daniel, Christopher

Title

A path dependent quantum approximate optimization algorithm optimized by pairwise correlation of angles

Physical Description

1 online resource (40 pages) : PDF

Date

2021

Degree Granting Institution

University of North Carolina at Charlotte

Abstract

Given the current promise of quantum computing to increase the efficiency of optimization algorithms, it is important to utilize these quantum algorithms for useful applications. The quantum approximate optimization algorithm was recently developed to accommodate combinatorial optimization problems where the minimum of a cost function is required for an optimal solution. We consider appropriate cost Hamiltonians of the long-range spin glass Ising model with the objectives to solve for an unknown a priori ground state and an unknown sequence of unitary operators to move an initial Hadamard quantum state to an arbitrary eigenstate of the Hamiltonian. We utilize a path dependent quantum approximate optimization algorithm optimized by considering the pairwise correlation of angles on its path to the global optimum of the entire angle parameter space. An importance sampling technique is used to distribute the probability of selecting a specific pair of angles to optimize along its path as it evolves with the depth of the quantum circuit. We also simulate the measurement process classically to resemble the sample outputs of a quantum computer and to determine how the sampling affects the performance of this algorithm. Lastly, results are demonstrated to justify this new approach to the quantum approximate optimization algorithm as a viable technique to solve quantum computational optimization problems.

Genre

masters theses

Subjects--Topics

Physics

Degree

M.S.

Subject Area

Applied Physics

Advisor(s)

Jacobs, Donald

Committee Members

Hofmann, Tino
Zhang, Yong

Degree Note

Thesis (M.S.)--University of North Carolina at Charlotte, 2021.

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Rights Holder Information

Copyright is held by the author unless otherwise indicated.

Identifier

Daniel_uncc_0694N_12899

Permalink

http://hdl.handle.net/20.500.13093/etd:2861