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arXiv · 2508.01496

Homology, Hopf Algebras and Quantum Code Surgery

Alexander Cowtan
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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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Alexander Cowtan. 2025-08-02. Homology, Hopf Algebras and Quantum Code Surgery. https://arxiv.org/abs/2508.01496

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