Implementing and Characterizing a Quantum Divide and Conquer Variational Quantum Algorithm

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Gray, A. (2022). Implementing and Characterizing a Quantum Divide and Conquer Variational Quantum Algorithm. Unc Charlotte Electronic Theses And Dissertations.
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Abstract

The current landscape of quantum computing devices consists of Noisy Intermediate-Scale Quantum (NISQ) devices, which contain around 100 or less qubits and are not fault-tolerant or error correcting. Due to the physical limitations of these devices, algorithms must be developed with short circuit depths and which are stable to the noise inherent to quantum measurements. A broad class of quantum computing algorithms called Variational Quantum Algorithms (VQAs), which leverage a classical computer for parameter optimization of a problem-related cost function, fit these criteria and serve as the basis for many NISQ-era algorithms. In this work, we develop a VQA based on a newly discovered set of operators called Divide And Conquer Operators (DACOs), which is termed the DACO-VQA. Using these operators, unitary parameter-dependent quantum gates can be constructed which, when consecutively applied on an initial Hadamard state, continually cut the Hilbert space in half, leading to a single pure state bit string in the end. This property is leveraged in the DACO-VQA to restrict the search to consecutive halves of the problem-Hilbert space, reducing the range of measurement sampling. The DACO-VQA also utilizes a cost function based on a partition function of the empirically measured energies of the states generated by the quantum computer. In this work we discuss the development of the DACO-VQA structure and its operators, as well as completeness of the operator pool chosen for the DACO-VQA, entangling capability of the quantum circuits utilized, and benchmark the performance of the algorithm for certain problem-Hamiltonians.

Details
Author

Gray, Alexander

Title

Implementing and Characterizing a Quantum Divide and Conquer Variational Quantum Algorithm

Physical Description

1 online resource (56 pages) : PDF

Date

2022

Degree Granting Institution

University of North Carolina at Charlotte

Abstract

The current landscape of quantum computing devices consists of Noisy Intermediate-Scale Quantum (NISQ) devices, which contain around 100 or less qubits and are not fault-tolerant or error correcting. Due to the physical limitations of these devices, algorithms must be developed with short circuit depths and which are stable to the noise inherent to quantum measurements. A broad class of quantum computing algorithms called Variational Quantum Algorithms (VQAs), which leverage a classical computer for parameter optimization of a problem-related cost function, fit these criteria and serve as the basis for many NISQ-era algorithms. In this work, we develop a VQA based on a newly discovered set of operators called Divide And Conquer Operators (DACOs), which is termed the DACO-VQA. Using these operators, unitary parameter-dependent quantum gates can be constructed which, when consecutively applied on an initial Hadamard state, continually cut the Hilbert space in half, leading to a single pure state bit string in the end. This property is leveraged in the DACO-VQA to restrict the search to consecutive halves of the problem-Hilbert space, reducing the range of measurement sampling. The DACO-VQA also utilizes a cost function based on a partition function of the empirically measured energies of the states generated by the quantum computer. In this work we discuss the development of the DACO-VQA structure and its operators, as well as completeness of the operator pool chosen for the DACO-VQA, entangling capability of the quantum circuits utilized, and benchmark the performance of the algorithm for certain problem-Hamiltonians.

Genre

masters theses

Subjects--Topics

Physics
Quantum theory

Degree

M.S.

Keywords

Divide And Conquer
Entanglement
Physics
Quantum Computing
Quantum Mechanics
Variational Quantum Algorithm

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, 2022.

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Rights Holder Information

Copyright is held by the author unless otherwise indicated.

Identifier

Gray_uncc_0694N_13229

Permalink

http://hdl.handle.net/20.500.13093/etd:3020