135,993 research outputs found
Quantum system characterization with limited resources
The construction and operation of large scale quantum information devices
presents a grand challenge. A major issue is the effective control of coherent
evolution, which requires accurate knowledge of the system dynamics that may
vary from device to device. We review strategies for obtaining such knowledge
from minimal initial resources and in an efficient manner, and apply these to
the problem of characterization of a qubit embedded into a larger state
manifold, made tractable by exploiting prior structural knowledge. We also
investigate adaptive sampling for estimation of multiple parameters
Quantum control theory and applications: A survey
This paper presents a survey on quantum control theory and applications from
a control systems perspective. Some of the basic concepts and main developments
(including open-loop control and closed-loop control) in quantum control theory
are reviewed. In the area of open-loop quantum control, the paper surveys the
notion of controllability for quantum systems and presents several control
design strategies including optimal control, Lyapunov-based methodologies,
variable structure control and quantum incoherent control. In the area of
closed-loop quantum control, the paper reviews closed-loop learning control and
several important issues related to quantum feedback control including quantum
filtering, feedback stabilization, LQG control and robust quantum control.Comment: 38 pages, invited survey paper from a control systems perspective,
some references are added, published versio
Newton algorithm for Hamiltonian characterization in quantum control
We propose a Newton algorithm to characterize the Hamiltonian of a quantum
system interacting with a given laser field. The algorithm is based on the
assumption that the evolution operator of the system is perfectly known at a
fixed time. The computational scheme uses the Crank-Nicholson approximation to
explicitly determine the derivatives of the propagator with respect to the
Hamiltonians of the system. In order to globalize this algorithm, we use a
continuation method that improves its convergence properties. This technique is
applied to a two-level quantum system and to a molecular one with a double-well
potential. The numerical tests show that accurate estimates of the unknown
parameters are obtained in some cases. We discuss the numerical limits of the
algorithm in terms of basin of convergence and non uniqueness of the solution.Comment: 18 pages, 7 figure
Orbits of quantum states and geometry of Bloch vectors for -level systems
Physical constraints such as positivity endow the set of quantum states with
a rich geometry if the system dimension is greater than two. To shed some light
on the complicated structure of the set of quantum states, we consider a
stratification with strata given by unitary orbit manifolds, which can be
identified with flag manifolds. The results are applied to study the geometry
of the coherence vector for n-level quantum systems. It is shown that the
unitary orbits can be naturally identified with spheres in R^{n^2-1} only for
n=2. In higher dimensions the coherence vector only defines a non-surjective
embedding into a closed ball. A detailed analysis of the three-level case is
presented. Finally, a refined stratification in terms of symplectic orbits is
considered.Comment: 15 pages LaTeX, 3 figures, reformatted, slightly modified version,
corrected eq.(3), to appear in J. Physics
Quantum System Identification by Bayesian Analysis of Noisy Data: Beyond Hamiltonian Tomography
We consider how to characterize the dynamics of a quantum system from a
restricted set of initial states and measurements using Bayesian analysis.
Previous work has shown that Hamiltonian systems can be well estimated from
analysis of noisy data. Here we show how to generalize this approach to systems
with moderate dephasing in the eigenbasis of the Hamiltonian. We illustrate the
process for a range of three-level quantum systems. The results suggest that
the Bayesian estimation of the frequencies and dephasing rates is generally
highly accurate and the main source of errors are errors in the reconstructed
Hamiltonian basis.Comment: 6 pages, 3 figure
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