Quantum error correcting codes with local verification and high reliability
Good Quantum Locally Testable Codes from Product Expansion
Computational ComplexityInformation Theory
Summary
Quantum computers need ways to detect and correct errors that happen while they work. This paper shows how to build special quantum codes that can be checked locally and still keep good performance on lots of measures like error detection and efficiency. The authors build these codes by combining advanced math structures with special classical codes called Reed-Solomon codes. This approach depends on a certain mathematical assumption but leads to codes that are easier to test without reading everything.
What this means in practice
- •For quantum hardware developers: Enable more efficient error checking in quantum devices by using codes that allow local tests with guaranteed error detection and correction strength.
- •For cryptographic system builders: Provide new types of quantum error correcting codes that improve reliability of quantum communication and cryptography protocols under certain mathematical constructions.
A theory result. No direct application yet.
Authors
Mitali Bafna, Anqi Li, Quynh T. Nguyen
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.