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Quantum Computation and Information Storage in Quantum Double Models

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. http://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.))
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)
Research Advisor(s):
  • Preskill, John P.
Group:Institute for Quantum Information and Matter, IQIM
Thesis Committee:
  • Preskill, John P. (chair)
  • Chen, Xie
  • Kitaev, Alexei
  • Endres, Manuel A.
Defense Date:3 May 2018
Funders:
Funding AgencyGrant Number
National Science FoundationPHY-1125565
National Science FoundationPHY-0803371
Gordon and Betty Moore FoundationGBMF-2644
Gordon and Betty Moore FoundationGBMF-12500028
Record Number:CaltechTHESIS:05232018-150514177
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:05232018-150514177
DOI:10.7907/KMJ2-1307
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevA.93.052337DOIPaper on which second chapter is based.
http://dx.doi.org/10.1103/PhysRevB.96.195150DOIPaper on which third chapter is based.
http://arxiv.org/abs/1805.00032arXivPaper on which fourth chapter is based.
http://maxpixel.freegreatpicture.com/Alice-In-Wonderland-Vintage-Book-Illustration-1794700OtherSource of image on page iii.
ORCID:
AuthorORCID
Kómár, Anna0000-0002-4701-4931
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:06 Jun 2018 16:53

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