Quantum signal processing by single-qubit dynamics
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017. === Cataloged from PDF version of thesis. === Includes bibliographical references (pages 117-125). === Quantum computation is the most powerful realizable model of computation, and is uniquely positioned to solve spe...
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ndltd-MIT-oai-dspace.mit.edu-1721.1-1150252019-05-02T16:34:03Z Quantum signal processing by single-qubit dynamics Low, Guang Hao Isaac L. Chuang. Massachusetts Institute of Technology. Department of Physics. Massachusetts Institute of Technology. Department of Physics. Physics. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017. Cataloged from PDF version of thesis. Includes bibliographical references (pages 117-125). Quantum computation is the most powerful realizable model of computation, and is uniquely positioned to solve specialized problems intractable to classical computers. This quantum advantage arises from directly exploiting the strangeness of quantum mechanics that is fundamental to reality. As such, one expects our understanding of quantum processes in physical systems to be indispensable to the design and execution of quantum algorithms. We present quantum signal processing, which exploits the dynamics of simple quantum systems to perform non-trivial computations. Such systems applied as computational modules in larger quantum algorithms, offer a natural physical alternative to standard tasks such as the calculation of elementary functions with integer arithmetic. The quantum advantage of this approach, based on simple physics, is of significant practical relevance. In cases, arbitrary bits of precision may be emulated using only constant space. Moreover, the simplicity and performance of quantum signal processing is such that it is the final missing ingredient for realizing a number of optimal quantum algorithms, particularly in Hamiltonian simulation. Quantum signal processing realizes a useful fusion of analog and digital models of quantum computation. At the physical level, we focus on how even a simple two-level system - the qubit, computes through optimal discrete-time quantum control. Whereas quantum control is typically used to synthesize unitary quantum gates, we solve the synthesis problem of unitary quantum functions with a fully characterization of achievable functions, and efficient techniques for their implementation. This furnishes a surprisingly rich framework in the analog model of quantum computation for computing functions. The generality of this model is realized by many applications, often with no modification, to quantum algorithms designed for digital quantum computers, in particular for matrix manipulation. In this manner, we solve a number of open problem related to optimal amplitude amplification algorithms, optimally computing on matrices with a quantum computer, and the simulation of physical systems. by Guang Hao Low. Ph. D. 2018-04-27T18:10:33Z 2018-04-27T18:10:33Z 2017 2017 Thesis http://hdl.handle.net/1721.1/115025 1031219672 eng MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582 125 pages application/pdf Massachusetts Institute of Technology |
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Physics. Low, Guang Hao Quantum signal processing by single-qubit dynamics |
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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2017. === Cataloged from PDF version of thesis. === Includes bibliographical references (pages 117-125). === Quantum computation is the most powerful realizable model of computation, and is uniquely positioned to solve specialized problems intractable to classical computers. This quantum advantage arises from directly exploiting the strangeness of quantum mechanics that is fundamental to reality. As such, one expects our understanding of quantum processes in physical systems to be indispensable to the design and execution of quantum algorithms. We present quantum signal processing, which exploits the dynamics of simple quantum systems to perform non-trivial computations. Such systems applied as computational modules in larger quantum algorithms, offer a natural physical alternative to standard tasks such as the calculation of elementary functions with integer arithmetic. The quantum advantage of this approach, based on simple physics, is of significant practical relevance. In cases, arbitrary bits of precision may be emulated using only constant space. Moreover, the simplicity and performance of quantum signal processing is such that it is the final missing ingredient for realizing a number of optimal quantum algorithms, particularly in Hamiltonian simulation. Quantum signal processing realizes a useful fusion of analog and digital models of quantum computation. At the physical level, we focus on how even a simple two-level system - the qubit, computes through optimal discrete-time quantum control. Whereas quantum control is typically used to synthesize unitary quantum gates, we solve the synthesis problem of unitary quantum functions with a fully characterization of achievable functions, and efficient techniques for their implementation. This furnishes a surprisingly rich framework in the analog model of quantum computation for computing functions. The generality of this model is realized by many applications, often with no modification, to quantum algorithms designed for digital quantum computers, in particular for matrix manipulation. In this manner, we solve a number of open problem related to optimal amplitude amplification algorithms, optimally computing on matrices with a quantum computer, and the simulation of physical systems. === by Guang Hao Low. === Ph. D. |
author2 |
Isaac L. Chuang. |
author_facet |
Isaac L. Chuang. Low, Guang Hao |
author |
Low, Guang Hao |
author_sort |
Low, Guang Hao |
title |
Quantum signal processing by single-qubit dynamics |
title_short |
Quantum signal processing by single-qubit dynamics |
title_full |
Quantum signal processing by single-qubit dynamics |
title_fullStr |
Quantum signal processing by single-qubit dynamics |
title_full_unstemmed |
Quantum signal processing by single-qubit dynamics |
title_sort |
quantum signal processing by single-qubit dynamics |
publisher |
Massachusetts Institute of Technology |
publishDate |
2018 |
url |
http://hdl.handle.net/1721.1/115025 |
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AT lowguanghao quantumsignalprocessingbysinglequbitdynamics |
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