Efficient quantum error correction for fully correlated noise

Chi Kwong Li; Mikio Nakahara; Yiu Tung Poon; Nung Sing Sze; Hiroyuki Tomita

doi:10.1016/j.physleta.2011.07.027

Efficient quantum error correction for fully correlated noise

Chi Kwong Li, Mikio Nakahara, Yiu Tung Poon, Nung Sing Sze, Hiroyuki Tomita

Research output: Journal article publication › Journal article › Academic research › peer-review

17 Citations (Scopus)

Abstract

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 σx⊗n, σy⊗nand σz⊗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 an error-free encoding, which encode (n-2) data qubits when n is even. Quantum circuits implementing these schemes are constructed.

Original language	English
Pages (from-to)	3255-3258
Number of pages	4
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	375
Issue number	37
DOIs	https://doi.org/10.1016/j.physleta.2011.07.027
Publication status	Published - 29 Aug 2011

Keywords

Higher rank numerical range
Mixed unitary channel
Quantum error correction
Recovery operator

ASJC Scopus subject areas

General Physics and Astronomy

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10.1016/j.physleta.2011.07.027

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AU - Li, Chi Kwong

AU - Nakahara, Mikio

AU - Poon, Yiu Tung

AU - Sze, Nung Sing

AU - Tomita, Hiroyuki

PY - 2011/8/29

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AB - 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 σx⊗n, σy⊗nand σz⊗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 an error-free encoding, which encode (n-2) data qubits when n is even. Quantum circuits implementing these schemes are constructed.

KW - Higher rank numerical range

KW - Mixed unitary channel

KW - Quantum error correction

KW - Recovery operator

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JO - Physics Letters, Section A: General, Atomic and Solid State Physics

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ER -

Efficient quantum error correction for fully correlated noise

Abstract

Keywords

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