Homology, Hopf Algebras and Quantum Code Surgery
Alexander Cowtan
TL;DR
This thesis explores algebraic methods for quantum error correction and fault-tolerant quantum computation, generalizing known code constructions and formalizing protocols like lattice surgery using advanced mathematical frameworks.
Contribution
It introduces new algebraic techniques for fault-tolerant quantum computation and provides a rigorous formalization of quantum code constructions and protocols.
Findings
New algebraic methods for fault-tolerant quantum computation
Formalization of quantum code constructions
Generalization of existing quantum code protocols
Abstract
This thesis is a study of quantum error-correction codes from an algebraic perspective. We concern ourselves not only with quantum codes but also protocols to perform logical quantum computation using such codes. We derive new methods of performing fault-tolerant quantum computation, rooted in abstract algebra and category theory. We also generalise known constructions of quantum codes and rigorously formalise existing constructions. At its core, this thesis asks: what is lattice surgery?
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Taxonomy
TopicsQuantum Computing Algorithms and Architecture · Polynomial and algebraic computation · Complexity and Algorithms in Graphs