Efficient Quantum Error Correction for Fully Correlated Noise

Details Efficient Quantum Error Correction for Fully Correlated Noise Efficient Quantum Error Correction for Fully Correlated Noise

2011-04-25

arxiv.org/abs/1104.4750v2

Phys. Lett. A, 375:3255-3258 (2011)

Physics

Quantum Physics

11 pages, 2 figures

Scientific paper

10.1016/j.physleta.2011.07.027

We investigate an efficient quantum error correction of a fully correlated noise. Suppose the noise is characterized by a quantum channel whose error operators take fully correlated forms given by $\sigma_x^{\otimes n}$, $\sigma_y^{\otimes n}$ and $\sigma_z^{\otimes n}$, where $n>2$ is the number of qubits encoding the codeword. It is proved that (i) $n$ qubits codeword encodes $(n-1)$ data qubits when $n$ is odd and (ii) $n$ qubits codeword implements a noiseless subsystem encoding $(n-2)$ data qubits when $n$ is even. Quantum circuits implementing these schemes are constructed.

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