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The ABCs of the Color Code: A Study of Topological Quantum Codes as Toy Models for Fault-Tolerant Quantum Computation and Quantum Phases Of Matter


Kubica, Aleksander Marek (2018) The ABCs of the Color Code: A Study of Topological Quantum Codes as Toy Models for Fault-Tolerant Quantum Computation and Quantum Phases Of Matter. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/059V-MG69.


This thesis is devoted to studying a class of quantum error-correcting codes — topological quantum codes. We explore the question of how one can achieve fault- tolerant quantum computation with topological codes. We treat quantum error-correcting codes not only as a compelling ingredient needed to build a quantum computer, but also as a useful theoretical tool in other areas of physics. In particular, we explore what insights topological codes can provide into challenging questions, such as the classification of quantum phases of matter.

In this thesis, we focus on a family of topological codes — color codes, which are particularly intriguing due to the rich physics they display and their computational power. We start by introducing color codes and explaining their basic properties. Then, we show how to perform fault-tolerant universal quantum computation with three-dimensional color codes by transverse gates and code switching. We later compare the resource overhead of the code-switching approach with that of a state distillation scheme. We discuss how to perform error correction with the toric and color codes, as well as introduce local decoders for those two families of codes. By exploiting a connection between error correction and statistical mechanics we estimate the storage threshold error rates for bit-flip and phase-flip noise in the three-dimensional color code. We finish by showing that the color and toric code families in d dimensions are equivalent in a sense of local unitary transformations and explore implications of this equivalence.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:quantum information; quantum computation; quantum many-body physics; quantum error correction; topological quantum codes
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
Thesis Committee:
  • Preskill, John P. (chair)
  • Alicea, Jason F.
  • Brandao, Fernando
  • Kitaev, Alexei
Defense Date:8 June 2017
Record Number:CaltechTHESIS:05282018-173928314
Persistent URL:
Related URLs:
URLURL TypeDescription covered in Ch. 2 covered in Ch. 5 covered in Ch. 6
Kubica, Aleksander Marek0000-0001-8213-8190
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10955
Deposited By: Aleksander Kubica
Deposited On:29 May 2018 19:58
Last Modified:08 Aug 2022 17:50

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