A note on the minimum distance of quantum LDPC codes
Nicolas Delfosse, Zhentao Li, St\'ephan Thomass\'e
TL;DR
This paper establishes an exponential lower bound on the minimum distance of certain quantum LDPC codes derived from Cayley graphs, advancing beyond previous quadratic bounds through combinatorial analysis.
Contribution
It introduces a new exponential lower bound on the minimum distance of quantum LDPC codes based on Cayley graphs, improving prior quadratic bounds.
Findings
Exponential lower bound on code minimum distance
Improved theoretical understanding of quantum LDPC codes
Analysis of subsets satisfying parity conditions
Abstract
We provide a new lower bound on the minimum distance of a family of quantum LDPC codes based on Cayley graphs proposed by MacKay, Mitchison and Shokrollahi. Our bound is exponential, improving on the quadratic bound of Couvreur, Delfosse and Z\'emor. This result is obtained by examining a family of subsets of the hypercube which locally satisfy some parity conditions.
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Taxonomy
TopicsError Correcting Code Techniques · Quantum Computing Algorithms and Architecture · Cooperative Communication and Network Coding