Singleton-bound approaching AQECC[1] 

Description

Approximate quantum code of rate \(R\) that can tolerate adversarial errors nearly saturating the quantum Singleton bound of \((1-R)/2\). The formulation of such codes relies on a notion of quantum list decoding. Sampling a description of this code can be done with an efficient randomized algorithm with \(2^{-\Omega(n)}\) failure probability.

Protection

For any \(\gamma>0\) and rate \(0<R<1\), these approximate quantum \([[n,R \cdot n]]_q\) codes have constant Galois-qudit dimension \(q=q(\gamma)\) and correct errors acting on \((1-R-\gamma) \cdot n/2\) registers, up to a recovery error of \(2^{-\Omega(n)}\).

Rate

Given rate \(R\), tolerate adversarial errors nearly saturating the quantum Singleton bound of \((1-R)/2\).

Encoding

Efficient encoding.

Decoding

Quantum list decodable [1].

Parents

Cousins

References

[1]
T. Bergamaschi, L. Golowich, and S. Gunn, “Approaching the Quantum Singleton Bound with Approximate Error Correction”, (2022) arXiv:2212.09935
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Zoo Code ID: quantum_singleton

Cite as:
“Singleton-bound approaching AQECC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/quantum_singleton
BibTeX:
@incollection{eczoo_quantum_singleton, title={Singleton-bound approaching AQECC}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/quantum_singleton} }
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https://errorcorrectionzoo.org/c/quantum_singleton

Cite as:

“Singleton-bound approaching AQECC”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/quantum_singleton

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/qudits_galois/stabilizer/css/quantum_singleton.yml.