1,673 research outputs found
Complete controllability of finite-level quantum systems
Complete controllability is a fundamental issue in the field of control of
quantum systems, not least because of its implications for dynamical
realizability of the kinematical bounds on the optimization of observables. In
this paper we investigate the question of complete controllability for
finite-level quantum systems subject to a single control field, for which the
interaction is of dipole form. Sufficient criteria for complete controllability
of a wide range of finite-level quantum systems are established and the
question of limits of complete controllability is addressed. Finally, the
results are applied to give a classification of complete controllability for
four-level systems.Comment: 14 pages, IoP-LaTe
Limitations on quantum control
In this note we give an introduction to the topic of quantum control,
explaining what its objectives are, and describing some of its limitations.Comment: 6 page
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
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
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
Implementation of Fault-tolerant Quantum Logic Gates via Optimal Control
The implementation of fault-tolerant quantum gates on encoded logic qubits is
considered. It is shown that transversal implementation of logic gates based on
simple geometric control ideas is problematic for realistic physical systems
suffering from imperfections such as qubit inhomogeneity or uncontrollable
interactions between qubits. However, this problem can be overcome by
formulating the task as an optimal control problem and designing efficient
algorithms to solve it. In particular, we can find solutions that implement all
of the elementary logic gates in a fixed amount of time with limited control
resources for the five-qubit stabilizer code. Most importantly, logic gates
that are extremely difficult to implement using conventional techniques even
for ideal systems, such as the T-gate for the five-qubit stabilizer code, do
not appear to pose a problem for optimal control.Comment: 18 pages, ioptex, many 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]
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