Approaching the Quantum Singleton Bound with Approximate Error Correction
5Louis Golowich (UC Berkeley)
https://simons.berkeley.edu/talks/louis-golowich-uc-berkeley-2023-07-14
Quantum Summer Cluster Workshop
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.
Joint work with Thiago Bergamaschi and Sam Gunn.