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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