Elena Berardini, Reza Dastbasteh, Josu Etxezarreta Martinez, Shreyas Jain, Olatz Sanz Larrarte (Dec 12 2024).

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.

Arxiv: https://arxiv.org/abs/2412.08586