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
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