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Quantum Error Correction via Less Noisy Qubits

Quantum Error Correction via Less Noisy Qubits Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit any classical linear codes over the binary or quaternary finite field. However, the known entanglement-assisted scheme requires noiseless qubits that help correct quantum errors on noisy qubits, which can be too severe an assumption. We prove that a more relaxed and realistic assumption is sufficient by presenting encoding and decoding operations assisted by qubits on which quantum errors of one particular kind may occur. As in entanglement assistance, our scheme can import any binary or quaternary linear codes. If the auxiliary qubits are noiseless, our codes become entanglement-assisted codes, and saturate the quantum Singleton bound when the underlying classical codes are maximum distance separable. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review Letters American Physical Society (APS)

Quantum Error Correction via Less Noisy Qubits

Physical Review Letters , Volume 110 (17) – Apr 22, 2013
5 pages

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References (35)

Publisher
American Physical Society (APS)
Copyright
© 2013 American Physical Society
ISSN
0031-9007
DOI
10.1103/PhysRevLett.110.170501
pmid
23679693
Publisher site
See Article on Publisher Site

Abstract

Known quantum error correction schemes are typically able to take advantage of only a limited class of classical error-correcting codes. Entanglement-assisted quantum error correction is a partial solution which made it possible to exploit any classical linear codes over the binary or quaternary finite field. However, the known entanglement-assisted scheme requires noiseless qubits that help correct quantum errors on noisy qubits, which can be too severe an assumption. We prove that a more relaxed and realistic assumption is sufficient by presenting encoding and decoding operations assisted by qubits on which quantum errors of one particular kind may occur. As in entanglement assistance, our scheme can import any binary or quaternary linear codes. If the auxiliary qubits are noiseless, our codes become entanglement-assisted codes, and saturate the quantum Singleton bound when the underlying classical codes are maximum distance separable.

Journal

Physical Review LettersAmerican Physical Society (APS)

Published: Apr 22, 2013

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