Entanglement-assisted quantum low-density parity-check codes

TL;DR

This paper introduces a combinatorial design-based method for constructing entanglement-assisted quantum LDPC codes that achieve high performance, low complexity, and flexible entanglement requirements, including many new code families.

Contribution

It presents a general, combinatorial framework for creating entanglement-assisted quantum LDPC codes with desirable properties and many new code constructions.

Findings

Produces infinitely many new codes with various parameters.

Achieves high error correction performance and low decoding complexity.

Includes codes with better block error rates in simulations.

Abstract

This paper develops a general method for constructing entanglement-assisted quantum low-density parity-check (LDPC) codes, which is based on combinatorial design theory. Explicit constructions are given for entanglement-assisted quantum error-correcting codes (EAQECCs) with many desirable properties. These properties include the requirement of only one initial entanglement bit, high error correction performance, high rates, and low decoding complexity. The proposed method produces infinitely many new codes with a wide variety of parameters and entanglement requirements. Our framework encompasses various codes including the previously known entanglement-assisted quantum LDPC codes having the best error correction performance and many new codes with better block error rates in simulations over the depolarizing channel. We also determine important parameters of several well-known classes of quantum and classical LDPC codes for previously unsettled cases.