Asymptotically good CSS-T codes exist

• URL: http://arxiv.org/abs/2412.08586v1
• Date: Wed, 11 Dec 2024 18:03:58 GMT
• Title: Asymptotically good CSS-T codes exist
• Authors: Elena Berardini, Reza Dastbasteh, Josu Etxezarreta Martinez, Shreyas Jain, Olatz Sanz Larrarte,
• Abstract summary: We give a new construction of binary quantum codes that enables the generation of a CSS-T code from any given CSS code. We show that the same result holds for binary quantum low-density parity check CSS-T codes.
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• Abstract: We give a new construction of binary quantum codes that enables the generation of a CSS-T code from any given CSS code. Using this construction, we prove the existence of asymptotically good binary CSS-T codes, resolving a previously open problem in the literature. Furthermore, we demonstrate that the same result holds for binary quantum low-density parity check CSS-T codes, and establish the existence of asymptotically good CSS codes that support any given $Z$ rotation transversally. Finally, we analyze the structure of the logical operators corresponding to certain non-Clifford gates supported by the quantum codes obtained from our construction.

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