The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure

TL;DR

This paper presents a step-by-step design procedure for concatenated quantum error correction codes using EXIT charts, exemplified by a novel Quantum Irregular Convolutional Code that approaches the hashing bound within 0.4 dB.

Contribution

It introduces a new design methodology for quantum codes leveraging EXIT charts and proposes a flexible quantum irregular convolutional code for near-optimal quantum error correction.

Findings

QIRCC can be dynamically adapted to match inner codes.

The proposed design operates within 0.4 dB of the quantum noise limit.

EXIT chart-based design effectively approaches the hashing bound.

Abstract

Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed by exploiting a concatenated code structure, which invokes iterative decoding. Therefore, in this paper we provide an extensive step-by-step tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided concatenated quantum codes based on the underlying quantum-to-classical isomorphism. These design lessons are then exemplified in the context of our proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the outer component of a concatenated quantum code. The proposed QIRCC can be dynamically adapted to match any given inner code using EXIT charts, hence achieving a performance close to the hashing bound. It is demonstrated that our QIRCC-based optimized design is capable of operating within 0.4 dB of the noise limit.