Quantum Information Processing, Vol. 3, Nos. 1–5, October 2004 (© 2004)
Quantum Computing and Information Extraction for
Dynamical Quantum Systems
and Simone Montangero
Received February 2, 2004; accepted April 7, 2004
We discuss the simulation of complex dynamical systems on a quantum com-
puter. We show that a quantum computer can be used to efﬁciently extract rel-
evant physical information. It is possible to simulate the dynamical localization
of classical chaos and extract the localization length with quadratic speed up
with respect to any known classical computation. We can also compute with alge-
braic speed up the diffusion coefﬁcient and the diffusion exponent, both in the
regimes of Brownian and anomalous diffusion. Finally, we show that it is possi-
ble to extract the ﬁdelity of the quantum motion, which measures the stability of
the system under perturbations, with exponential speed up. The so-called quantum
sawtooth map model is used as a test bench to illustrate these results.
KEY WORDS: Quantum computation; quantum simulation; information
extraction; dynamical systems; complex systems; chaos.
PACS: 03.67.Lx; 05.45.Mt.
One of the main applications of computers is the simulation of dynamical
models describing the evolution of complex systems. From the viewpoint
of quantum computation, quantum mechanical systems play a special role.
Indeed, the simulation of quantum many-body problems on a classical
Center for Nonlinear and Complex Systems, Universit
a degli Studi dell’Insubria, Via Val-
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