High performance entanglement-assisted quantum LDPC codes need little entanglement

TL;DR

This paper demonstrates that high-performance entanglement-assisted quantum LDPC codes can be constructed with minimal entanglement, challenging the belief that large entanglement consumption is necessary for good codes.

Contribution

It introduces families of EAQECCs with entanglement consumption rates decreasing linearly with code length, including some requiring only one entangled state regardless of size.

Findings

Families of EAQECCs with low entanglement consumption are effective.

Numerical simulations show high performance of the proposed codes.

The work suggests practical implementation of entanglement-assisted quantum codes.

Abstract

Though the entanglement-assisted formalism provides a universal connection between a classical linear code and an entanglement-assisted quantum error-correcting code (EAQECC), the issue of maintaining large amount of pure maximally entangled states in constructing EAQECCs is a practical obstacle to its use. It is also conjectured that the power of entanglement-assisted formalism to convert those good classical codes comes from massive consumption of maximally entangled states. We show that the above conjecture is wrong by providing families of EAQECCs with an entanglement consumption rate that diminishes linearly as a function of the code length. Notably, two families of EAQECCs constructed in the paper require only one copy of maximally entangled state no matter how large the code length is. These families of EAQECCs that are constructed from classical finite geometric LDPC codes perform very well according to our numerical simulations. Our work indicates that EAQECCs are not only theoretically interesting, but also physically implementable. Finally, these high performance entanglement-assisted LDPC codes with low entanglement consumption rates allow one to construct high-performance standard QECCs with very similar parameters.