Quantum Information Processing, Vol. 5, No. 6, December 2006 (© 2006)
Dephasing of Quantum Bits by a Quasi-Static
J. M. Taylor
and M. D. Lukin
Received December 20, 2005; accepted December 31, 2005; Published online August 29, 2006
We examine coherent processes in a two-state quantum system that is strongly
coupled to a mesoscopic spin bath and weakly coupled to other environmental
degrees of freedom. Our analysis is speciﬁcally aimed at understanding the quan-
tum dynamics of solid-state quantum bits such as electron spins in semiconductor
structures and superconducting islands. The role of mesoscopic degrees of free-
dom with long correlation times (local degrees of freedom such as nuclear spins
and charge traps) in qubit-related dephasing is discussed in terms of a quasi-
static bath. A mathematical framework simultaneously describing coupling to the
slow mesoscopic bath and a Markovian environment is developed and the dephas-
ing and decoherence properties of the total system are investigated. The model is
applied to several speciﬁc examples with direct relevance to current experiments.
Comparisons to experiments suggests that such quasi-static degrees of freedom
play an important role in current qubit implementations. Several methods of
mitigating the bath-induced error are considered.
KEY WORDS: Spin bath; decoherence; dephasing; quantum bit; quantum dot;
PACS: 03.65.Yz, 03.67.-a, 73.21.La, 74.78.Na.
Solid-state quantum information research attempts the difﬁcult task of
separating a few local degrees of freedom from a strongly coupled envi-
ronment. This necessitates a clever choice of logical basis to minimize
the dominant couplings and environmental preparation through cooling.
Electron spin in quantum dots has been suggested as a quantum bit,
Dedicated to Anton Zeilinger, whose work has inspired exploration of quantum
phenomenon in many avenues of physics and beyond.
Department of Physics, Harvard University, Cambridge, MA 02138 USA.
To whom correspondence should be addressed. Email: email@example.com
1570-0755/06/1200-0503/0 © 2006 Springer Science+Business Media, Inc.