Quantum Precoded Polar Codes

TL;DR

This paper introduces a new family of quantum CSS codes derived from precoded polar codes, optimized via genetic algorithms, achieving low logical error rates comparable to surface codes.

Contribution

It presents a novel quantum coding scheme combining polar codes with precoding and genetic optimization, improving quantum error correction performance.

Findings

Codes of dimensions [\[256, 2\\]] and [\[512, 2\\]] are constructed.

Logical error rates are similar to those of surface codes.

Optimization of rate profile and precoder enhances code performance.

Abstract

We introduce a new family of CSS codes obtained from rate-1 precoded polar codes, which harnesses the precoding benefits obtained for classical short blocklength polar codes. We optimize the rate profile and precoder of these codes with a genetic algorithm, and present codes of dimension $ [\![256, 2 ]\!] $ and $ [\![512, 2]\!] $ that have logical error rates similar to the $ [\![1201, 1, 25 ]\!] $ surface code over the depolarizing channel.