Interpolation of Quantum Polar Codes and Quantum Reed-Muller Codes

TL;DR

This paper introduces methods to interpolate between quantum polar and Reed-Muller codes, aiming to develop practical quantum error-correcting codes with better finite-size performance and without entanglement assistance.

Contribution

It proposes strategies to interpolate quantum polar and Reed-Muller codes, addressing key limitations and enhancing code validity and performance.

Findings

Improved finite-size performance of quantum codes.

Valid quantum codes without entanglement assistance.

Enhanced decoding strategies for quantum codes.

Abstract

Good quantum error-correcting codes that fulfill practical considerations, such as simple encoding circuits and efficient decoders, are essential for functional quantum information processing systems. Quantum polar codes satisfy some of these requirements but lack certain critical features, thereby hindering their widespread use. Existing constructions either require entanglement assistance to produce valid quantum codes, suffer from poor finite-size performance, or fail to tailor polar codes to the underlying channel properties. Meanwhile, quantum Reed-Muller (RM) codes demonstrate strong performance, though no known efficient decoding algorithm exists for them. In this work, we propose strategies to interpolate between quantum polar codes and quantum RM codes, thus addressing the challenges of designing valid quantum polar codes without entanglement assistance and improving finite-size code performance.