Approaching the Quantum Singleton Bound with Approximate Error Correction
Symposium on the Theory of Computing (STOC)（2024）CCF A
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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Key words
Quantum Error Correction,Quantum Secret Sharing
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