On Transversality Across Two Distinct Quantum Error Correction Codes For Quantum Repeaters

TL;DR

This paper explores the transversality properties of CSS code pairs for quantum repeaters, proposing different codes for different stations and establishing conditions for non-local CNOT and CZ transversality.

Contribution

It introduces new conditions for CSS code pairs to be non-local CNOT and CZ transversal, and suggests using diverse codes across stations for improved quantum repeater performance.

Findings

Different stations can experience different errors, justifying diverse code use.

Less restrictive conditions than code identity are needed for non-local CNOT transversality.

Established conditions for CZ-transversality of CSS code pairs.

Abstract

In this paper, we investigate the transversality of pairs of CSS codes and their use in the second generation of quantum repeaters (QR)s. We show that different stations of quantum link can experience different errors. Considering this fact, we suggest to use different CSS codes in different stations. We also suggest to use $[[n, k]]$ codes with $k > 1$ as they are more efficient then codes with $k = 1$. We establish sufficient and necessary conditions for a pair of CSS codes to be non-local CNOT-transversal. We show that in contrast to the well known CNOT transversality which states that two CSS codes should be the same, less restrictive constraints are needed. Next, we establish sufficient and necessary conditions for a code pair to be CZ-transversal.