Approaching the Quantum Singleton Bound with Approximate Error Correction

Understand

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.