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arXiv · 1310.4401

Recursive encoding and decoding of the noiseless subsystem for qudits

Utkan Güngördü·Chi-Kwong Li·Mikio Nakahara·Yiu-Tung Poon·Nung-Sing Sze
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Abstract

We give a full explanation of the noiseless subsystem that protects a single-qubit against collective errors and the corresponding recursive scheme described by C.-K. Li et. al. [Phys. Rev. A 84, 044301 (2011)] from a representation theory point of view. Furthermore, we extend the construction to qudits under the influence of collective SU($d$) errors. We find that under this recursive scheme, the asymptotic encoding rate is $1/d$.

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Utkan Güngördü, Chi-Kwong Li, Mikio Nakahara, Yiu-Tung Poon, Nung-Sing Sze. 2014-04-04. Recursive encoding and decoding of the noiseless subsystem for qudits. https://doi.org/10.1103/physreva.89.042301

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