DeepAI

# Quantum LDPC codes with Ω(√(n)log^kn) distance, for any k

In this work we construct quantum LDPC codes of distance √(n)log^k n for any k, improving a recent result of Evra et. al. <cit.>. The work of <cit.> took advantage of the high dimensional expansion notion known as cosystolic expansion, that occurs in Ramanujan complexes. Our improvement is achieved by considering tensor product of Ramanujan complexes. The main conceptual contribution of our work is the following: a tensor product of a cosystolic expander with a complex with a linear cosystole has a linear cosystole.

• 17 publications
• 4 publications
12/07/2020

### Quantum LDPC Codes with Almost Linear Minimum Distance

We give a construction of quantum LDPC codes of dimension Θ(log N) and d...
12/01/2020

### Asymmetric Quantum Concatenated and Tensor Product Codes with Large Z-Distances

In many quantum channels, dephasing errors occur more frequently than th...
08/13/2020

### Dynamic Complexity of Expansion

Dynamic Complexity was introduced by Immerman and Patnaik <cit.> (see al...
08/18/2022

### Memory and Capacity of Graph Embedding Methods

This paper analyzes the graph embedding method introduced in <cit.>, whi...
12/22/2020

### A generalization of the construction of quantum codes from Hermitian self-orthogonal codes

An important strength of the q-ary stabilizer quantum codes is that they...
05/10/2021

### Tamper Detection against Unitary Operators

We consider (Enc, Dec) schemes which are used to encode a classical/quan...
06/20/2022

### Two-sided Robustly Testable Codes

We show that the tensor product of two random linear codes is robustly t...