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

• URL: http://arxiv.org/abs/2406.00350v1
• Date: Sat, 1 Jun 2024 08:04:51 GMT
• Title: On Transversality Across Two Distinct Quantum Error Correction Codes For Quantum Repeaters
• Authors: Mahdi Bayanifar, Alexei Ashikhmin, Dawei Jiao, Olav Tirkkonen,
• Abstract summary: We show that different stations of quantum can experience different errors. Considering this fact, we suggest to use different CSS codes in different stations. We show that in contrast to the well known CNOTity which states that two CSS codes should be the same, less restrictive constraints are needed.
• Score: 7.38597648387724
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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