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Paper 1

Hardness of decoding quantum stabilizer codes

Pavithran Iyer, David Poulin

Year

2013

Journal

arXiv preprint

DOI

arXiv:1310.3235

arXiv

1310.3235

In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the decoding problem consists of determining the most likely recovery given the syndrome. The corresponding classical problem is known to be NP-complete, and a similar decoding problem for quantum codes is also known to be NP-complete. However, this decoding strategy is not optimal in the quantum setting as it does not take into account error degeneracy, which causes distinct errors to have the same effect on the code. Here, we show that optimal decoding of stabilizer codes is computationally much harder than optimal decoding of classical linear codes, it is #P.

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Paper 2

Fault tolerance with noisy and slow measurements and preparation.

Paz-Silva GA, Brennen GK, Twamley J.

Year

2010

Journal

Phys Rev Lett

DOI

10.1103/physrevlett.105.100501

arXiv

-

No abstract.

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