3,722 research outputs found
Implementation of Quantum Gates via Optimal Control
Starting with the basic control system model often employed in NMR pulse
design, we derive more realistic control system models taking into account
effects such as off-resonant excitation for systems with fixed inter-qubit
coupling controlled by globally applied electromagnetic fields, as well as for
systems controlled by a combination of a global fields and local control
electrodes. For both models optimal control is used to find controls that
implement a set of two- and three-qubit gates with fidelity greater than
99.99%. While in some cases the optimal pulses obtained appear to be
surprisingly simple and experimentally realistic, the results also show that
the "optimal" pulses obtained in other cases are experimentally infeasible, and
more sophisticated parametrization of the control fields and numerical
algorithms are needed.Comment: 10 pages, 4 figure
Fast, high fidelity information transmission through spin chain quantum wires
Spin chains have been proposed as quantum wires for information transfer in
solid state quantum architectures. We show that huge gains in both transfer
speed and fidelity are possible using a minimalist control approach that relies
only a single, local, on-off switch actuator. Effective switching time
sequences can be determined using optimization techniques for both ideal and
disordered chains. Simulations suggest that effective optimization is possible
even in the absence of accurate models.Comment: revtex4, 4 pages, 5 figure
Degrees of controllability for quantum systems and applications to atomic systems
Precise definitions for different degrees of controllability for quantum
systems are given, and necessary and sufficient conditions are discussed. The
results are applied to determine the degree of controllability for various
atomic systems with degenerate energy levels and transition frequencies.Comment: 20 pages, IoP LaTeX, revised and expanded versio
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
Criteria for reachability of quantum states
We address the question of which quantum states can be inter-converted under
the action of a time-dependent Hamiltonian. In particular, we consider the
problem applied to mixed states, and investigate the difference between pure
and mixed-state controllability introduced in previous work. We provide a
complete characterization of the eigenvalue spectrum for which the state is
controllable under the action of the symplectic group. We also address the
problem of which states can be prepared if the dynamical Lie group is not
sufficiently large to allow the system to be controllable.Comment: 14 pages, IoP LaTeX, first author has moved to Cambridge university
([email protected]
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
Control of non-controllable quantum systems: A quantum control algorithm based on Grover iteration
A new notion of controllability, eigenstate controllability, is defined for
finite-dimensional bilinear quantum mechanical systems which are neither
strongly completely controllably nor completely controllable. And a quantum
control algorithm based on Grover iteration is designed to perform a quantum
control task of steering a system, which is eigenstate controllable but may not
be (strongly) completely controllable, from an arbitrary state to a target
state.Comment: 7 pages, no figures, submitte
Limits of control for quantum systems: kinematical bounds on the optimization of observables and the question of dynamical realizability
In this paper we investigate the limits of control for mixed-state quantum
systems. The constraint of unitary evolution for non-dissipative quantum
systems imposes kinematical bounds on the optimization of arbitrary
observables. We summarize our previous results on kinematical bounds and show
that these bounds are dynamically realizable for completely controllable
systems. Moreover, we establish improved bounds for certain partially
controllable systems. Finally, the question of dynamical realizability of the
bounds for arbitary partially controllable systems is shown to depend on the
accessible sets of the associated control system on the unitary group U(N) and
the results of a few control computations are discussed briefly.Comment: 5 pages, orginal June 30, 2000, revised September 28, 200
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