# Approaching the Quantum Singleton Bound with Approximate Error Correction.

STOC 2024 Proceedings of the 56th Annual ACM Symposium on Theory of Computing（2024）

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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