Quantum Information Processing, Vol. 6, No. 4, August 2007 (© 2007)
Quantum Error Correction of Time-correlated Errors
and Dan C. Marinescu
Received April 7, 2007; accepted May 24, 2007; Published online: July 7, 2007
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
and | 1
are entangled states of 2
basis states in H
KEY WORDS: quantum information; error correction; time-correlated;
PAC S: 03.67.-a; 03.67.Pp; 03.65.-w.
1. QUANTUM ERROR CORRECTION
Quantum states are subject to decoherence and the question whether a
reliable quantum computer could be built was asked early on. A “pure
state” | ϕ=α
| 1 may be transformed as a result of the interac-
tion with the environment into a “mixed state” with density matrix:
ρ =| α
| 00 |+|α
| 11 | .
Other forms of decoherence, e.g., leakage may affect the state probability
amplitude as well.
The initial thought was that a quantum computation could only be
carried out successfully if its duration is shorter than the decoherence time
School of Electrical Engineering and Computer Science, University of Central
Florida, P. O. Box 162362, Orlando, FL 32816-2362, USA. E-mails: email@example.com;
To whom correspondence should be addressed.
1570-0755/07/0800-0273/0 © 2007 Springer Science+Business Media, LLC