@inproceedings{6660dd26e7aa46c6a0ca6c9f6cdf105f,
title = "Expansion of High-Dimensional Cubical Complexes: with Application to Quantum Locally Testable Codes",
abstract = "We introduce a high-dimensional cubical complex, for any dimension t in N, and apply it to the design of quantum locally testable codes. Our complex is a natural generalization of the constructions by Panteleev and Kalachev and by Dinur et. al of a square complex (case t=2), which have been applied to the design of classical locally testable codes (LTC) and quantum low-density parity check codes (qLDPC) respectively. We turn the geometric (cubical) complex into a chain complex by relying on constant-sized local codes H_{1}, ·,ht as gadgets. A recent result of Panteleev and Kalachev on existence of tuples of codes that are product expanding enables us to prove lower bounds on the cycle and co-cycle expansion of our chain complex. For t=4 our construction gives a new family of 'almost-good' quantum LTCs - with constant relative rate, inverse-polylogarithmic relative distance and soundness, and constant-size parity checks. Both the distance of the quantum code and its local testability are proven directly from the cycle and co-cycle expansion of our chain complex.",
author = "Irit Dinur and Lin, {Ting Chun} and Thomas Vidick",
note = "Publisher Copyright: {\textcopyright} 2024 IEEE.; 65th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2024 ; Conference date: 27-10-2024 Through 30-10-2024",
year = "2024",
doi = "https://doi.org/10.1109/FOCS61266.2024.00031",
language = "الإنجليزيّة",
series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",
publisher = "IEEE Computer Society",
pages = "379--385",
booktitle = "Proceedings - 2024 IEEE 65th Annual Symposium on Foundations of Computer Science, FOCS 2024",
address = "الولايات المتّحدة",
}