143 research outputs found
Minimization of length and curvature on planar curves
In this paper we consider the problem of reconstructing a curve that is partially hidden or corrupted by minimizing the functional ∫ √1+K 2 ds, depending both on length and curvature K. We fix starting and ending points as well as initial and final directions. For this functional, we find non-existence of minimizers on various functional spaces in which the problem is naturally formulated. In this case, minimizing sequences of trajectories can converge to curves with angles. We instead prove existence of minimizers for the "time-reparameterized" functional ∫γ(t)√1+Kγ2 dt for all boundary conditions if initial and final directions are considered regardless to orientation. ©2009 IEEE
On optimum Hamiltonians for state transformations
For a prescribed pair of quantum states |psi_I> and |psi_F> we establish an
elementary derivation of the optimum Hamiltonian, under constraints on its
eigenvalues, that generates the unitary transformation |psi_I> --> |psi_F> in
the shortest duration. The derivation is geometric in character and does not
rely on variational calculus.Comment: 5 page
Adiabatic passage and ensemble control of quantum systems
This paper considers population transfer between eigenstates of a finite
quantum ladder controlled by a classical electric field. Using an appropriate
change of variables, we show that this setting can be set in the framework of
adiabatic passage, which is known to facilitate ensemble control of quantum
systems. Building on this insight, we present a mathematical proof of
robustness for a control protocol -- chirped pulse -- practiced by
experimentalists to drive an ensemble of quantum systems from the ground state
to the most excited state. We then propose new adiabatic control protocols
using a single chirped and amplitude shaped pulse, to robustly perform any
permutation of eigenstate populations, on an ensemble of systems with badly
known coupling strengths. Such adiabatic control protocols are illustrated by
simulations achieving all 24 permutations for a 4-level ladder
Sub-Finsler Structures from the Time-Optimal Control Viewpoint for some Nilpotent Distributions
In this paper, we study the sub-Finsler geometry as a time-optimal control problem. In particular, we consider non-smooth and non-strictly convex sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet distributions. Motivated by problems in geometric group theory, we characterize extremal curves, discuss their optimality, and calculate the metric spheres, proving their Euclidean rectifiability. © 2016, Springer Science+Business Media New York
Effect of feedback on the control of a two-level dissipative quantum system
We show that it is possible to modify the stationary state by a feedback
control in a two-level dissipative quantum system. Based on the geometric
control theory, we also analyze the effect of the feedback on the time-optimal
control in the dissipative system governed by the Lindblad master equation.
These effects are reflected in the function and
that characterize the optimal trajectories, as well as the
switching function and which characterize the switching
point in time for the time-optimal trajectory.Comment: 5 pages, 5 figure
Time-Optimal Adiabatic-Like Expansion of Bose-Einstein Condensates
In this paper we study the fast adiabatic-like expansion of a one-dimensional
Bose-Einstein condensate (BEC) confined in a harmonic potential, using the
theory of time-optimal control. We find that under reasonable assumptions
suggested by the experimental setup, the minimum-time expansion occurs when the
frequency of the potential changes in a bang-bang form between the permitted
values. We calculate the necessary expansion time and show that it scales
logarithmically with large values of the expansion factor. This work is
expected to find applications in areas where the efficient manipulations of BEC
is of utmost importance. As an example we present the field of atom
interferometry with BEC, where the wavelike properties of atoms are used to
perform interference experiments that measure with unprecedented precision
small shifts induced by phenomena like rotation, acceleration, and gravity
gradients.Comment: Submitted to 51st IEEE Conference on Decision and Contro
Comment on "Control landscapes are almost always trap free: a geometric assessment"
We analyze a recent claim that almost all closed, finite dimensional quantum
systems have trap-free (i.e., free from local optima) landscapes (B. Russell
et.al. J. Phys. A: Math. Theor. 50, 205302 (2017)). We point out several errors
in the proof which compromise the authors' conclusion.
Interested readers are highly encouraged to take a look at the "rebuttal"
(see Ref. [1]) of this comment published by the authors of the criticized work.
This "rebuttal" is a showcase of the way the erroneous and misleading
statements under discussion will be wrapped up and injected in their future
works, such as R. L. Kosut et.al, arXiv:1810.04362 [quant-ph] (2018).Comment: 6 pages, 1 figur
Optimal quantum control in nanostructures: Theory and application to generic three-level system
Coherent carrier control in quantum nanostructures is studied within the
framework of Optimal Control. We develop a general solution scheme for the
optimization of an external control (e.g., lasers pulses), which allows to
channel the system's wavefunction between two given states in its most
efficient way; physically motivated constraints, such as limited laser
resources or population suppression of certain states, can be accounted for
through a general cost functional. Using a generic three-level scheme for the
quantum system, we demonstrate the applicability of our approach and identify
the pertinent calculation and convergence parameters.Comment: 7 pages; to appear in Phys. Rev.
Implementing Quantum Gates using the Ferromagnetic Spin-J XXZ Chain with Kink Boundary Conditions
We demonstrate an implementation scheme for constructing quantum gates using
unitary evolutions of the one-dimensional spin-J ferromagnetic XXZ chain. We
present numerical results based on simulations of the chain using the
time-dependent DMRG method and techniques from optimal control theory. Using
only a few control parameters, we find that it is possible to implement one-
and two-qubit gates on a system of spin-3/2 XXZ chains, such as Not, Hadamard,
Pi-8, Phase, and C-Not, with fidelity levels exceeding 99%.Comment: Updated Acknowledgement
Optimal control of quantum superpositions in a bosonic Josephson junction
We show how to optimally control the creation of quantum superpositions in a
bosonic Josephson junction within the two-site Bose-Hubbard model framework.
Both geometric and purely numerical optimal control approaches are used, the
former providing a generalization of the proposal of Micheli et al [Phys. Rev.
A 67, 013607 (2003)]. While this method is shown not to lead to significant
improvements in terms of time of formation and fidelity of the superposition, a
numerical optimal control approach appears more promising, as it allows to
create an almost perfect superposition, within a time short compared to other
existing protocols. We analyze the robustness of the optimal solution against
atom number variations. Finally, we discuss to which extent these optimal
solutions could be implemented with the state of art technology.Comment: Several comments added, structure re-organize
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