# Quantum Error Correction of Time-correlated Errors

Quantum Error Correction of Time-correlated Errors The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of quantum systems; an error corrected during the previous cycle may reoccur later due to physical processes specific for each physical implementation of the qubits. In this paper, we study quantum error correction for a restricted class of time-correlated errors in a spin-boson model. The algorithm we propose allows the correction of two errors per error correction cycle, provided that one of them is time-correlated. The algorithm can be applied to any stabilizer code when the two logical qubits $$\mid {\rm 0}_L \rangle$$ and $$\mid {\rm 1}_L \rangle$$ are entangled states of 2 n basis states in $${\mathcal{H}}_{2^n}$$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Quantum Error Correction of Time-correlated Errors

, Volume 6 (4) – Jul 7, 2007
21 pages

/lp/springer_journal/quantum-error-correction-of-time-correlated-errors-OPAQL3efPZ
Publisher
Springer Journals
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-007-0058-1
Publisher site
See Article on Publisher Site

### Abstract

The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of quantum systems; an error corrected during the previous cycle may reoccur later due to physical processes specific for each physical implementation of the qubits. In this paper, we study quantum error correction for a restricted class of time-correlated errors in a spin-boson model. The algorithm we propose allows the correction of two errors per error correction cycle, provided that one of them is time-correlated. The algorithm can be applied to any stabilizer code when the two logical qubits $$\mid {\rm 0}_L \rangle$$ and $$\mid {\rm 1}_L \rangle$$ are entangled states of 2 n basis states in $${\mathcal{H}}_{2^n}$$ .

### Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 7, 2007

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