On Cayley Graphs, Surface Codes, and the Limits of Homological Coding for Quantum Error Correction

DOI10.1007/978-3-642-01877-0_21zbMath1248.94128OpenAlexW1531594186MaRDI QIDQ5323014

Gilles Zémor

Publication date: 23 July 2009

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-01877-0_21

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Other types of codes (94B60) Quantum coding (general) (81P70)

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Isoperimetric inequalities for Ramanujan complexes and topological expanders ⋮ Homology-changing percolation transitions on finite graphs ⋮ Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds ⋮ Decodable Quantum LDPC Codes beyond the $\sqrt{n}$ Distance Barrier Using High-Dimensional Expanders ⋮ On tensor products of CSS codes ⋮ Topological quantum codes from self-complementary self-dual graphs ⋮ Channel polarization of two-dimensional-input quantum symmetric channels ⋮ Building manifolds from quantum codes ⋮ Hypermap-homology quantum codes ⋮ New classes of quantum codes on closed orientable surfaces ⋮ Systole of congruence coverings of arithmetic hyperbolic manifolds ⋮ Bounding the distance of quantum surface codes

Cites Work

• Self-dual random-plaquette gauge model and the quantum toric code
• Explicit constructions of graphs without short cycles and low density codes
• The Moore bound for irregular graphs
• Triangle group representations and constructions of regular maps
• On the Error-Correcting Capabilities of Cycle Codes of Graphs
• Multiple-particle interference and quantum error correction
• Homological error correction: Classical and quantum codes
• Sparse-Graph Codes for Quantum Error Correction
• Optimal Cycle Codes Constructed From Ramanujan Graphs
• Topological quantum memory
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