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arXiv · 2212.09935

Approaching the Quantum Singleton Bound with Approximate Error Correction

Thiago Bergamaschi·Louis Golowich·Sam Gunn
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Abstract

It is well known that no quantum error correcting code of rate $R$ can correct adversarial errors on more than a $(1-R)/4$ fraction of symbols. But what if we only require our codes to *approximately* recover the message? We construct efficiently-decodable approximate quantum codes against adversarial error rates approaching the quantum Singleton bound of $(1-R)/2$, for any constant rate $R$. Moreover, the size of the alphabet is a constant independent of the message length and the recovery error is exponentially small in the message length. Central to our construction is a notion of quantum list decoding and an implementation involving folded quantum Reed-Solomon codes.

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Thiago Bergamaschi, Louis Golowich, Sam Gunn. 2022-12-20. Approaching the Quantum Singleton Bound with Approximate Error Correction. https://arxiv.org/abs/2212.09935

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