92,607 research outputs found
Optimal Control Theory for Continuous Variable Quantum Gates
We apply the methodology of optimal control theory to the problem of
implementing quantum gates in continuous variable systems with quadratic
Hamiltonians. We demonstrate that it is possible to define a fidelity measure
for continuous variable (CV) gate optimization that is devoid of traps, such
that the search for optimal control fields using local algorithms will not be
hindered. The optimal control of several quantum computing gates, as well as
that of algorithms composed of these primitives, is investigated using several
typical physical models and compared for discrete and continuous quantum
systems. Numerical simulations indicate that the optimization of generic CV
quantum gates is inherently more expensive than that of generic discrete
variable quantum gates, and that the exact-time controllability of CV systems
plays an important role in determining the maximum achievable gate fidelity.
The resulting optimal control fields typically display more complicated Fourier
spectra that suggest a richer variety of possible control mechanisms. Moreover,
the ability to control interactions between qunits is important for delimiting
the total control fluence. The comparative ability of current experimental
protocols to implement such time-dependent controls may help determine which
physical incarnations of CV quantum information processing will be the easiest
to implement with optimal fidelity.Comment: 39 pages, 11 figure
Analytical results for the multi-objective design of model-predictive control
In model-predictive control (MPC), achieving the best closed-loop performance
under a given computational resource is the underlying design consideration.
This paper analyzes the MPC design problem with control performance and
required computational resource as competing design objectives. The proposed
multi-objective design of MPC (MOD-MPC) approach extends current methods that
treat control performance and the computational resource separately -- often
with the latter as a fixed constraint -- which requires the implementation
hardware to be known a priori. The proposed approach focuses on the tuning of
structural MPC parameters, namely sampling time and prediction horizon length,
to produce a set of optimal choices available to the practitioner. The posed
design problem is then analyzed to reveal key properties, including smoothness
of the design objectives and parameter bounds, and establish certain validated
guarantees. Founded on these properties, necessary and sufficient conditions
for an effective and efficient solver are presented, leading to a specialized
multi-objective optimizer for the MOD-MPC being proposed. Finally, two
real-world control problems are used to illustrate the results of the design
approach and importance of the developed conditions for an effective solver of
the MOD-MPC problem
Synthesis of Minimal Error Control Software
Software implementations of controllers for physical systems are at the core
of many embedded systems. The design of controllers uses the theory of
dynamical systems to construct a mathematical control law that ensures that the
controlled system has certain properties, such as asymptotic convergence to an
equilibrium point, while optimizing some performance criteria. However, owing
to quantization errors arising from the use of fixed-point arithmetic, the
implementation of this control law can only guarantee practical stability:
under the actions of the implementation, the trajectories of the controlled
system converge to a bounded set around the equilibrium point, and the size of
the bounded set is proportional to the error in the implementation. The problem
of verifying whether a controller implementation achieves practical stability
for a given bounded set has been studied before. In this paper, we change the
emphasis from verification to automatic synthesis. Using synthesis, the need
for formal verification can be considerably reduced thereby reducing the design
time as well as design cost of embedded control software.
We give a methodology and a tool to synthesize embedded control software that
is Pareto optimal w.r.t. both performance criteria and practical stability
regions. Our technique is a combination of static analysis to estimate
quantization errors for specific controller implementations and stochastic
local search over the space of possible controllers using particle swarm
optimization. The effectiveness of our technique is illustrated using examples
of various standard control systems: in most examples, we achieve controllers
with close LQR-LQG performance but with implementation errors, hence regions of
practical stability, several times as small.Comment: 18 pages, 2 figure
Cover-Encodings of Fitness Landscapes
The traditional way of tackling discrete optimization problems is by using
local search on suitably defined cost or fitness landscapes. Such approaches
are however limited by the slowing down that occurs when the local minima that
are a feature of the typically rugged landscapes encountered arrest the
progress of the search process. Another way of tackling optimization problems
is by the use of heuristic approximations to estimate a global cost minimum.
Here we present a combination of these two approaches by using cover-encoding
maps which map processes from a larger search space to subsets of the original
search space. The key idea is to construct cover-encoding maps with the help of
suitable heuristics that single out near-optimal solutions and result in
landscapes on the larger search space that no longer exhibit trapping local
minima. We present cover-encoding maps for the problems of the traveling
salesman, number partitioning, maximum matching and maximum clique; the
practical feasibility of our method is demonstrated by simulations of adaptive
walks on the corresponding encoded landscapes which find the global minima for
these problems.Comment: 15 pages, 4 figure
Fitness Uniform Optimization
In evolutionary algorithms, the fitness of a population increases with time
by mutating and recombining individuals and by a biased selection of more fit
individuals. The right selection pressure is critical in ensuring sufficient
optimization progress on the one hand and in preserving genetic diversity to be
able to escape from local optima on the other hand. Motivated by a universal
similarity relation on the individuals, we propose a new selection scheme,
which is uniform in the fitness values. It generates selection pressure toward
sparsely populated fitness regions, not necessarily toward higher fitness, as
is the case for all other selection schemes. We show analytically on a simple
example that the new selection scheme can be much more effective than standard
selection schemes. We also propose a new deletion scheme which achieves a
similar result via deletion and show how such a scheme preserves genetic
diversity more effectively than standard approaches. We compare the performance
of the new schemes to tournament selection and random deletion on an artificial
deceptive problem and a range of NP-hard problems: traveling salesman, set
covering and satisfiability.Comment: 25 double-column pages, 12 figure
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