Approaching the Quantum Singleton Bound with Approximate Error Correction

• URL: http://arxiv.org/abs/2212.09935v1
• Date: Tue, 20 Dec 2022 01:01:01 GMT
• Title: Approaching the Quantum Singleton Bound with Approximate Error Correction
• Authors: Thiago Bergamaschi, Louis Golowich, Sam Gunn
• Abstract summary: We construct efficiently-decodable approximate quantum codes against adversarial error rates approaching the quantum Singleton bound of $(1-R)/2$. The size of the alphabet is a constant independent of the message length and the recovery error is exponentially small in the message length.
• Score: 0.12891210250935148
• License: http://creativecommons.org/licenses/by/4.0/
• 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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