Quantum Computation and Information Storage in Quantum Double Models

• Main Author: Kómár, Anna
• Format: Others
• Published: 2018
• Online Access: https://thesis.library.caltech.edu/10926/1/KomarAnna2018.pdf; https://thesis.library.caltech.edu/10926/18/toriccode1.pdf; https://thesis.library.caltech.edu/10926/23/toriccode2.pdf; 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 <https://resolver.caltech.edu/CaltechTHESIS:05232018-150514177>

<p>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.</p> <p>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".</p> <p>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.</p> <p>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.</p>