61,772 research outputs found
Flatness-based control of a single qubit gate
This work considers the open-loop control problem of steering a two level
quantum system from an initial to a final condition. The model of this system
evolves on the state space SU(2), having two inputs that correspond to the
complex amplitude of a resonant laser field. A symmetry preserving flat output
is constructed using a fully geometric construction and quaternion
computations. Simulation results of this flatness-based open-loop control are
provided.Comment: Submitted to IEEE AC. Simulation code available at
http://cas.ensmp.fr/~rouchon/publications/PR2007/CodeMatlabScilabQubit.zi
A Time-Periodic Lyapunov Approach for Motion Planning of Controllable Driftless Systems on SU(n)
For a right-invariant and controllable driftless system on SU(n), we consider
a time-periodic reference trajectory along which the linearized control system
generates su(n): such trajectories always exist and constitute the basic
ingredient of Coron's Return Method. The open-loop controls that we propose,
which rely on a left-invariant tracking error dynamics and on a fidelity-like
Lyapunov function, are determined from a finite number of left-translations of
the tracking error and they assure global asymptotic convergence towards the
periodic reference trajectory. The role of these translations is to avoid being
trapped in the critical region of this Lyapunov-like function. The convergence
proof relies on a periodic version of LaSalle's invariance principle and the
control values are determined by numerical integration of the dynamics of the
system. Simulations illustrate the obtained controls for and the
generation of the C--NOT quantum gate.Comment: Submitte
Practical characterization of quantum devices without tomography
Quantum tomography is the main method used to assess the quality of quantum
information processing devices, but its complexity presents a major obstacle
for the characterization of even moderately large systems. The number of
experimental settings required to extract complete information about a device
grows exponentially with its size, and so does the running time for processing
the data generated by these experiments. Part of the problem is that tomography
generates much more information than is usually sought. Taking a more targeted
approach, we develop schemes that enable (i) estimating the fidelity of an
experiment to a theoretical ideal description, (ii) learning which description
within a reduced subset best matches the experimental data. Both these
approaches yield a significant reduction in resources compared to tomography.
In particular, we demonstrate that fidelity can be estimated from a number of
simple experimental settings that is independent of the system size, removing
an important roadblock for the experimental study of larger quantum information
processing units.Comment: (v1) 11 pages, 1 table, 4 figures. (v2) See also the closely related
work: arXiv:1104.4695 (v3) method extended to continuous variable systems
(v4) updated to published versio
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