2016/06/22 by Nicolas Delfosse, Delfosse, Nicolas, Pavithran Iyer +3 · 10 citations
Computer Science · Mathematics · Physics and Astronomy · #Code (set theory) #Coding theory and cryptography #Cohomology #Computer science #FOS: Computer and information sciences #FOS: Physical sciences #Generalization #Geometry #Homomorphism #Information Theory (cs.IT) #Lattice (music) #Mathematical analysis #Mathematics #Physics #Planar #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum computer #Quantum mechanics #Qubit #Set (abstract data type) #Surface (topology) #Theoretical physics #Toric code #cs.IT #math.IT #quant-ph #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1606.07116
published in arXiv (Cornell University) (Cornell University) · 28 pages
arxiv created 2016/06/22 · openalex publication_date 2016/06/22 · arxiv updated 2016/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
We consider a notion of relative homology (and cohomology) for surfaces with two types of boundaries. Using this tool, we study a generalization of Kitaev's code based on surfaces with mixed boundaries. This construction includes both Bravyi and Kitaev's and Freedman and Meyer's extension of Kitaev's toric code. We argue that our generalization offers a denser storage of quantum information. In a planar architecture, we obtain a three-fold overhead reduction over the standard architecture consisting of a punctured square lattice.