Bias-tailored quantum LDPC codes

Written comprehensive exam: Quantum LDPC Codes

Tailored Codes for Small Quantum Memories

A Novel Quantum Signature Scheme with Quantum LDPC Codes

This paper presents a novel quantum signature scheme by using quantum quasi-cyclic low density parity check (QC-LDPC) codes and quantum hash function. We construct quantum public keys by using quantum QC-LDPC Codes. Decoding general linear codes is NP-complete problem. The security of our scheme relies on the fact that NP-complete problem can not be solved on quantum Turing machines. Based on t...

A Note on the Minimum Distance of Quantum LDPC Codes

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 [13]. Our bound is exponential, improving on the quadratic bound of Couvreur, Delfosse and Zémor [3]. This result is obtained by examining a family of subsets of the hypercube which locally satisfy some parity conditions.

Constructions and performance of classes of quantum LDPC codes

Two methods for constructing quantum LDPC codes are presented. We explain how to overcome the difficulty of finding a set of low weight generators for the stabilizer group of the code. Both approaches are based on some graph representation of the generators of the stabilizer group and on simple local rules that ensure commutativity. A message passing algorithm for generic quantum LDPC codes is ...