576 research outputs found
On the Emergence of Nonextensivity at the Edge of Quantum Chaos
We explore the border between regular and chaotic quantum dynamics,
characterized by a power law decrease in the overlap between a state evolved
under chaotic dynamics and the same state evolved under a slightly perturbed
dynamics. This region corresponds to the edge of chaos for the classical map
from which the quantum chaotic dynamics is derived and can be characterized via
nonextensive entropy concepts.Comment: Invited paper to appear in "Decoherence and Entropy in Complex
Systems", ed. H.T. Elze, Lecture Notes in Physics (Springer, Heidelberg), in
press. 13 pages including 6 figures and 1 tabl
Fidelity Decay as an Efficient Indicator of Quantum Chaos
Recent work has connected the type of fidelity decay in perturbed quantum
models to the presence of chaos in the associated classical models. We
demonstrate that a system's rate of fidelity decay under repeated perturbations
may be measured efficiently on a quantum information processor, and analyze the
conditions under which this indicator is a reliable probe of quantum chaos and
related statistical properties of the unperturbed system. The type and rate of
the decay are not dependent on the eigenvalue statistics of the unperturbed
system, but depend on the system's eigenvector statistics in the eigenbasis of
the perturbation operator. For random eigenvector statistics the decay is
exponential with a rate fixed precisely by the variance of the perturbation's
energy spectrum. Hence, even classically regular models can exhibit an
exponential fidelity decay under generic quantum perturbations. These results
clarify which perturbations can distinguish classically regular and chaotic
quantum systems.Comment: 4 pages, 3 figures, LaTeX; published version (revised introduction
and discussion
Implementation of the Quantum Fourier Transform
The quantum Fourier transform (QFT) has been implemented on a three bit
nuclear magnetic resonance (NMR) quantum computer, providing a first step
towards the realization of Shor's factoring and other quantum algorithms.
Implementation of the QFT is presented with fidelity measures, and state
tomography. Experimentally realizing the QFT is a clear demonstration of NMR's
ability to control quantum systems.Comment: 6 pages, 2 figure
Quantum Process Tomography of the Quantum Fourier Transform
The results of quantum process tomography on a three-qubit nuclear magnetic
resonance quantum information processor are presented, and shown to be
consistent with a detailed model of the system-plus-apparatus used for the
experiments. The quantum operation studied was the quantum Fourier transform,
which is important in several quantum algorithms and poses a rigorous test for
the precision of our recently-developed strongly modulating control fields. The
results were analyzed in an attempt to decompose the implementation errors into
coherent (overall systematic), incoherent (microscopically deterministic), and
decoherent (microscopically random) components. This analysis yielded a
superoperator consisting of a unitary part that was strongly correlated with
the theoretically expected unitary superoperator of the quantum Fourier
transform, an overall attenuation consistent with decoherence, and a residual
portion that was not completely positive - although complete positivity is
required for any quantum operation. By comparison with the results of computer
simulations, the lack of complete positivity was shown to be largely a
consequence of the incoherent errors during the quantum process tomography
procedure. These simulations further showed that coherent, incoherent, and
decoherent errors can often be identified by their distinctive effects on the
spectrum of the overall superoperator. The gate fidelity of the experimentally
determined superoperator was 0.64, while the correlation coefficient between
experimentally determined superoperator and the simulated superoperator was
0.79; most of the discrepancies with the simulations could be explained by the
cummulative effect of small errors in the single qubit gates.Comment: 26 pages, 17 figures, four tables; in press, Journal of Chemical
Physic
Experimental Implementation of the Quantum Baker's Map
This paper reports on the experimental implementation of the quantum baker's
map via a three bit nuclear magnetic resonance (NMR) quantum information
processor. The experiments tested the sensitivity of the quantum chaotic map to
perturbations. In the first experiment, the map was iterated forward and then
backwards to provide benchmarks for intrinsic errors and decoherence. In the
second set of experiments, the least significant qubit was perturbed in between
the iterations to test the sensitivity of the quantum chaotic map to applied
perturbations. These experiments are used to investigate previous predicted
properties of quantum chaotic dynamics.Comment: submitted to PR
Implementation of Conditional Phase Shift gate for Quantum Information Processing by NMR, using Transition-selective pulses
Experimental realization of quantum information processing in the field of
nuclear magnetic resonance (NMR) has been well established. Implementation of
conditional phase shift gate has been a significant step, which has lead to
realization of important algorithms such as Grover's search algorithm and
quantum Fourier transform. This gate has so far been implemented in NMR by
using coupling evolution method. We demonstrate here the implementation of the
conditional phase shift gate using transition selective pulses. As an
application of the gate, we demonstrate Grover's search algorithm and quantum
Fourier transform by simulations and experiments using transition selective
pulses.Comment: 14 pages, 5 figure
Spintronics and Quantum Dots for Quantum Computing and Quantum Communication
Control over electron-spin states, such as coherent manipulation, filtering
and measurement promises access to new technologies in conventional as well as
in quantum computation and quantum communication. We review our proposal of
using electron spins in quantum confined structures as qubits and discuss the
requirements for implementing a quantum computer. We describe several
realizations of one- and two-qubit gates and of the read-in and read-out tasks.
We discuss recently proposed schemes for using a single quantum dot as
spin-filter and spin-memory device. Considering electronic EPR pairs needed for
quantum communication we show that their spin entanglement can be detected in
mesoscopic transport measurements using metallic as well as superconducting
leads attached to the dots.Comment: Prepared for Fortschritte der Physik special issue, Experimental
Proposals for Quantum Computation. 15 pages, 5 figures; typos corrected,
references adde
Dependence of ozone production on NO and hydrocarbons in the troposphere
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95525/1/grl10419.pd
The Edge of Quantum Chaos
We identify a border between regular and chaotic quantum dynamics. The border
is characterized by a power law decrease in the overlap between a state evolved
under chaotic dynamics and the same state evolved under a slightly perturbed
dynamics. For example, the overlap decay for the quantum kicked top is well
fitted with (with the nonextensive entropic
index and depending on perturbation strength) in the region
preceding the emergence of quantum interference effects. This region
corresponds to the edge of chaos for the classical map from which the quantum
chaotic dynamics is derived.Comment: 4 pages, 4 figures, revised version in press PR
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