Generalizing Quantum Tanner Codes

Olai Å. Mostad; Eirik Rosnes; Hsuan-Yin Lin

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arXiv · 2405.07980

Generalizing Quantum Tanner Codes

Olai Å. Mostad·Eirik Rosnes·Hsuan-Yin Lin

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Abstract

In this work, we present a generalization of the recently proposed quantum Tanner codes by Leverrier and Z\'emor, which contains a construction of asymptotically good quantum LDPC codes. Quantum Tanner codes have so far been constructed equivalently from groups, Cayley graphs, or square complexes constructed from groups. We show how to enlarge this to group actions on finite sets, Schreier graphs, and a family of square complexes which is the largest possible in a certain sense. Furthermore, we discuss how the proposed generalization opens up the possibility of finding other families of asymptotically good quantum codes.

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Olai Å. Mostad, Eirik Rosnes, Hsuan-Yin Lin. 2024-05-13. Generalizing Quantum Tanner Codes. https://arxiv.org/abs/2405.07980

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