Quantum Information Processing, Vol. 3, Nos. 1–5, October 2004 (© 2004)
Bang–Bang Refocusing of a Qubit Exposed
to Telegraph Noise
Frank K. Wilhelm,
William M. Kaminsky
and Seth Lloyd
Received February 1, 2004; accepted March 25, 2004
Solid state qubits promise the great advantage of being naturally scalable to large
quantum computer architectures, but they also possess the signiﬁcant disadvan-
tage of being intrinsically exposed to many sources of noise in the macroscopic
solid-state environment. With suitably chosen systems such as superconductors,
many of sources of noise can be suppressed. However, imprecision in nanofabri-
cation will inevitably induce defects and disorder, such as charged impurities in
the device material or substrate. Such defects generically produce telegraph noise
and can hence be modelled as bistable ﬂuctuators. We demonstrate the possibil-
ity of the active suppression of such telegraph noise by bang–bang control through
an exhaustive study of a qubit coupled to a single bistable ﬂuctuator. We use
a stochastic Schr
odinger equation, which is solved both numerically and analyt-
ically. The resulting dynamics can be visualized as diffusion of a spin vector on
the Bloch sphere. We ﬁnd that bang–bang control suppresses the effect of a bista-
ble ﬂuctuator by a factor roughly equalling the ratio of the bang–bang period and
the typical ﬂuctuator period. Therefore, we show the bang–bang protocol works
essentially as a high pass ﬁlter on the spectrum of such telegraph noise sources.
This suggests how the inﬂuence of 1/f -noise ubiquitous to the solid state world
could be reduced, as it is typically generated by an ensemble of bistable ﬂuctua-
tors. Finally, we develop random walk models that estimate the level of noise sup-
pression resulting from imperfect bang–bang operations, such as those that cannot
be treated as δ-function impulses and those that have phase and axis errors.
KEY WORDS: Bistable ﬂuctuator; telegraph noise; 1/f -noise; quantum con-
trol; random walk.
PACS: 03.65.Yz; 03.67.Lx; 05.40.-a.
Sektion Physik and CeNS, Ludwig-Maximilians-Universit
at, 80333 M
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139.
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge,
To whom correspondence should be addressed. E-mail: email@example.com-
1570-0755/04/1000-0247/0 © 2004 Springer Science+Business Media, Inc.