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Khovanov homology and quantum error-correcting codes

2024/10/15 by Milena Harned, Akhmechet, Rostislav, Harned, Milena +10
Computer Science · #57K18 #94B99 #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #Information Theory (cs.IT) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.2410.11252

openalex publication_date 2024/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

Error-correcting codes for quantum computing are crucial to address the fundamental problem of communication in the presence of noise and imperfections. Audoux used Khovanov homology to define families of quantum error-correcting codes with desirable properties. We explore Khovanov homology and some of its many extensions, namely reduced, annular, and \mathfraksl3 homology, to generate new families of quantum codes and to establish several properties about codes that arise in this way, such as behavior of distance under Reidemeister moves or connected sums.

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