Citation
Kómár, Anna (2018) Quantum Computation and Information Storage in Quantum Double Models. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KMJ2-1307. https://resolver.caltech.edu/CaltechTHESIS:05232018-150514177
Abstract
The results of this thesis concern the real-world realization of quantum computers, specifically how to build their "hard drives" or quantum memories. These are many-body quantum systems, and their building blocks are qubits, the same way bits are the building blocks of classical computers.
Quantum memories need to be robust against thermal noise, noise that would otherwise destroy the encoded information, similar to how strong magnetic field corrupts data classically stored in magnetic many-body systems (e.g., in hard drives). In this work I focus on a subset of many-body models, called quantum doubles, which, in addition to storing the information, could be used to perform the steps of the quantum computation, i.e., work as a "quantum processor".
In the first part of my thesis, I investigate how long a subset of quantum doubles (qudit surface codes) can retain the quantum information stored in them, referred to as their memory time. I prove an upper bound for this memory time, restricting the maximum possible performance of qudit surface codes.
Then, I analyze the structure of quantum doubles, and find two interesting properties. First, that the high-level description of doubles, utilizing only their quasi-particles to describe their states, disregards key components of their microscopic properties. In short, quasi-particles (anyons) of quantum doubles are not in a one-to-one correspondence with the energy eigenstates of their Hamiltonian. Second, by investigating phase transitions of a simple quantum double, D(S3), I map its phase diagram, and interpret the physical processes the theory undergoes through terms borrowed from the Landau theory of phase transitions.
Item Type: | Thesis (Dissertation (Ph.D.)) | |||||||||||||||
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Subject Keywords: | Physics; quantum information; quantum computation; anyons | |||||||||||||||
Degree Grantor: | California Institute of Technology | |||||||||||||||
Division: | Physics, Mathematics and Astronomy | |||||||||||||||
Major Option: | Physics | |||||||||||||||
Thesis Availability: | Public (worldwide access) | |||||||||||||||
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Group: | Institute for Quantum Information and Matter | |||||||||||||||
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Defense Date: | 3 May 2018 | |||||||||||||||
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Record Number: | CaltechTHESIS:05232018-150514177 | |||||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:05232018-150514177 | |||||||||||||||
DOI: | 10.7907/KMJ2-1307 | |||||||||||||||
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Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||||||||
ID Code: | 10926 | |||||||||||||||
Collection: | CaltechTHESIS | |||||||||||||||
Deposited By: | Anna Komar | |||||||||||||||
Deposited On: | 30 May 2018 18:27 | |||||||||||||||
Last Modified: | 28 Feb 2023 19:09 |
Thesis Files
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PDF (Complete Thesis)
- Final Version
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PDF (Figure 1.1 (a))
- Supplemental Material
See Usage Policy. 602kB | |
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PDF (Figure 1.1 (b))
- Supplemental Material
See Usage Policy. 701kB |
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