1,678 research outputs found
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
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
Dissipative "Groups" and the Bloch Ball
We show that a quantum control procedure on a two-level system including
dissipation gives rise to a semi-group corresponding to the Lie algebra
semi-direct sum gl(3,R)+R^3. The physical evolution may be modelled by the
action of this semi-group on a 3-vector as it moves inside the Bloch sphere, in
the Bloch ball.Comment: 4 pages. Proceedings of Group 24, Paris, July, 200
Dissipative Quantum Control
Nature, in the form of dissipation, inevitably intervenes in our efforts to
control a quantum system. In this talk we show that although we cannot, in
general, compensate for dissipation by coherent control of the system, such
effects are not always counterproductive; for example, the transformation from
a thermal (mixed) state to a cold condensed (pure state) can only be achieved
by non-unitary effects such as population and phase relaxation.Comment: Contribution to Proceedings of \emph{ICCSUR 8} held in Puebla,
Mexico, July 2003, based on talk presented by Allan Solomon (ca 8 pages,
latex, 1 latex figure, 2 pdf figures converted to eps, appear to cause some
trouble
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]
Quantum Control of Two-Qubit Entanglement Dissipation
We investigate quantum control of the dissipation of entanglement under
environmental decoherence. We show by means of a simple two-qubit model that
standard control methods - coherent or open-loop control - will not in general
prevent entanglement loss. However, we propose a control method utilising a
Wiseman-Milburn feedback/measurement control scheme which will effectively
negate environmental entanglement dissipation.Comment: 11 pages,4 figures, minor correctio
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
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
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