Problem
Research questions and friction points this paper is trying to address.
quantum locally testable codes
constant rate
distance
soundness
locality
Good Quantum Locally Testable Codes from Product Expansion
🤖 AI Summary
本文通过使用高维扩展框架和非阿贝尔立方复合体，结合精心挑选的Reed-Solomon局部码，构建了具有恒定速率、距离、可靠性和局部性的量子局部可测试码。
📝 Abstract
We construct quantum locally testable codes (LTCs) with constant rate, distance, soundness and locality under a variant of a product expansion conjecture of Bafna and Vyas about Reed-Solomon codes. In particular, we use the high-dimensional expansion framework of Dinur, Lin and Vidick for constructing quantum LTCs, instantiated with the non-Abelian cubical complexes of Rungtanapirom, Stix and Vdovina. Our code is obtained by equipping the complex with carefully chosen Reed-Solomon local codes whose symmetries are compatible with those of the complex.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Quantum Locally Testable Codes
Product Expansion
High-dimensional Expansion
Non-Abelian Cubical Complexes
Reed-Solomon Codes
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