Homology, Hopf Algebras and Quantum Code Surgery

Alexander Cowtan

Homology, Hopf Algebras and Quantum Code Surgery

Quantum Physics 2025-08-05 v1

Authors: Alexander Cowtan

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?

Keywords

quantum error correction hopf algebras quantum algebra

Cite

@article{arxiv.2508.01496,
  title  = {Homology, Hopf Algebras and Quantum Code Surgery},
  author = {Alexander Cowtan},
  journal= {arXiv preprint arXiv:2508.01496},
  year   = {2025}
}

Comments

296 pages, dissertation submitted towards the degree of DPhil in Computer Science

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