Exploring the top and bottom of the quantum control landscape

A controlled quantum system possesses a search landscape defined by the target physical objective as a function of the controls. This paper focuses on the landscape for the transition probability P(i → f) between the states of a finite level quantum system. Traditionally, the controls are applied fields; here, we extend the notion of control to also include the Hamiltonian structure, in the form of time independent matrix elements. Level sets of controls that produce the same transition probability value are shown to exist at the bottom P(i → f)=0.0 and top P(i → f)=1.0 of the landscape with the field and/or Hamiltonian structure as controls. We present an algorithm to continuously explore these level sets starting from an initial point residing at either extreme value of P(i → f). The technique can also identify control solutions that exhibit the desirable properties of (a) robustness at the top and (b) the ability to rapidly rise towards an optimal control from the bottom. Numerical simulations are presented to illustrate the varied control behavior at the top and bottom of the landscape for several simple model systems.     

Exploiting time-independent Hamiltonian structure as controls for manipulating quantum dynamics

The opportunities offered by utilizing time-independent Hamiltonian structure as controls are explored for manipulating quantum dynamics. Two scenarios are investigated using different manifestations of Hamiltonian structure to illustrate the generality of the concept. In scenario I, optimally shaped electrostatic potentials are generated to flexibly control electron scattering in a two-dimensional subsurface plane of a semiconductor. A simulation is performed showing the utility of optimally setting the individual voltages applied to a multi-pixel surface gate array in order to produce a spatially inhomogeneous potential within the subsurface scattering plane. The coherent constructive and destructive electron wave interferences are manipulated by optimally adjusting the potential shapes to alter the scattering patterns. In scenario II, molecular vibrational wave packets are controlled by means of optimally selecting the Hamiltonian structure in cooperation with an applied field. As an illustration of the concept, a collection (i.e., a level set) of dipole functions is identified where each member serves with the same applied electric field to produce the desired final transition probability. The level set algorithm additionally found Hamiltonian structure controls exhibiting desirable physical properties. The prospects of utilizing the applied field and Hamiltonian structure simultaneously as controls is also explored. The control scenarios I and II indicate the gains offered by algorithmically guided molecular or material discovery for manipulating quantum dynamics phenomenon.     

Synthesis and electrooptic properties of side‐chain methacrylate polymers containing a new azophenylbenzoxazole chromophore

The synthesis and characterization of four methacrylate copolymers obtained by radical addition polymerization of methyl methacrylate as well as a new methacrylate azophenylbenzoxazole chromophore in percentages of 10, 30, 50, and 70% were explored. The copolymers were amorphous and showed glass‐transition temperatures ranging from 132 to 146 °C. High‐quality polymer films were easily obtained by spin coating from N‐methylpyrrolidone solutions. Polymer films spun cast on iridium tin oxide (ITO) substrates were used in the electro‐optic (EO) experiments to evaluate the EO coefficients r₃₃ using the reflection technique. The measured values fell in the range of 1.7–3.7 pm/V (laser incident wavelength of 1.552 μm) depending on the percentage of chromophore in the polymer. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1162–1168, 2001     

Attaining persistent field-free control of open and closed quantum systems

Persistent quantum control (PQC) aims to maintain an observable objective value over a period of time following the action of an applied field. This paper assesses the feasibility of achieving PQC for arbitrary finite-level systems and observables. The analysis is carried out independent of the particular method used for state preparation. The PQC behavior is optimized over the set of physically accessible prepared states for both open and closed systems. The quality of observable value persistence in the postcontrol period was found to vary with the required duration of persistence, the system temperature, the chosen observable operator, and the energy levels of the system. The alignment of a rigid diatomic rotor is studied as a model system. The theoretical estimates of PQC behavior are encouraging and suggest feasible exploration in the laboratory using currently available technology.     

Why is chemical synthesis and property optimization easier than expected?

Identifying optimal conditions for chemical and material synthesis as well as optimizing the properties of the products is often much easier than simple reasoning would predict. The potential search space is infinite in principle and enormous in practice, yet optimal molecules, materials, and synthesis conditions for many objectives can often be found by performing a reasonable number of distinct experiments. Considering the goal of chemical synthesis or property identification as optimal control problems provides insight into this good fortune. Both of these goals may be described by a fitness function J that depends on a suitable set of variables (e.g., reactant concentrations, components of a material, processing conditions, etc.). The relationship between J and the variables specifies the fitness landscape for the target objective. Upon making simple physical assumptions, this work demonstrates that the fitness landscape for chemical optimization contains no local sub-optimal maxima that may hinder attainment of the absolute best value of J. This feature provides a basis to explain the many reported efficient optimizations of synthesis conditions and molecular or material properties. We refer to this development as OptiChem theory. The predicted characteristics of chemical fitness landscapes are assessed through a broad examination of the recent literature, which shows ample evidence of trap-free landscapes for many objectives. The fundamental and practical implications of OptiChem theory for chemistry are discussed.     

Potential drugs and nondrugs: prediction and identification of important structural features

Using decision trees, a model to discriminate between potential drugs and nondrugs has been developed. Compounds from the Available Chemical Directory and the World Drug Index databases were used as training set; the molecular structures were represented using extended atom types. The error rate on an independent validation data set is 17.4%. The number of false negatives can be reduced by penalizing the misclassification of drugs so that 92 out of 100 potential drugs are correctly recognized. At the same time, 34 out of 100 nondrugs are classified as potential drugs. The predictions of the model can be used to guide the purchase or selection of compounds for biological screening or the design of combinatorial libraries. The visualization of the generated models in the form of colored trees allowed us to identify a few, surprisingly simple features that explain the most significant differences between drugs and nondrugs in the training set: Just by testing the presence of hydroxyl, tertiary or secondary amino, carboxyl, phenol, or enol groups, already three quarters of all drugs could be correctly recognized. The nondrugs, on the other hand, are characterized by their aromatic nature with a low content of functional groups besides halogens. The general applicability of the model is shown by the predictions made for several Organon databases.     

Local topology at limited resource induced suboptimal traps on the quantum control landscape

In a quantum optimal control experiment a system is driven towards a target observable value with a tailored external field. The underlying quantum control landscape, defined by the observable as a function of the control variables, lacks suboptimal extrema upon satisfaction of certain physical assumptions. This favorable topology implies that upon climbing the landscape to seek an optimal control field, a steepest ascent algorithm should not halt prematurely at suboptimal critical points, or traps. One of the important aforementioned assumptions is that no limitations are imposed on the control resources. Constraints on the control restricts access to certain regions of the landscape, potentially preventing optimal performance through convergence to limited resource induced suboptimal traps. This work develops mathematical tools to explore the local landscape structure around suboptimal critical points. The landscape structure may be favorably altered by systematically relaxing the control resources. In this fashion, isolated suboptimal critical points may be transformed into extensive level sets and then to saddle points permitting further landscape ascent. Time-independent kinematic controls are employed as stand-ins for traditional dynamic controls to allow for performing a simpler constrained resource landscape analysis. The kinematic controls can be directly transferred to their dynamic counterparts at any juncture of the kinematic analysis. The numerical simulations employ a family of landscape exploration algorithms while imposing constraints on the kinematic controls. Particular algorithms are introduced to meet the goals of either climbing the landscape or seeking specific changes in the topology of the landscape by relaxing the control resources.     

Integrated receiver architectures for board-to-board free-space optical interconnects

In many computer and server communications copper cables and wires are currently being used for data transmission and interconnects. However, due to significant shortcomings, such as long transmission time, high noise level, unstable electrical properties, and high power consumption for cooling, researchers are increasingly turning their research interests toward alternatives, such as fiber optic interconnects and free-space optical communication technologies. In this paper, we present design considerations for an integrated receiver for high-speed free-space line-of-sight optical interconnects for distortion-free data transmission in an environment with mechanical vibrations and air turbulences. The receiver consists of an array of high-speed photodiodes for data communication and an array of quadrant photodiodes for real-time beam tracking in order to compensate for the beam misalignment caused by vibrations in servers. Different configurations for spatially positioning the quadrant and data photodiodes are discussed for 4×4 and 9×9 multielement optical detector arrays. We also introduce a new beam tracking device, termed the strip quadrant photodiodes, in order to accurately track highly focused optical beams with very small beam diameter.     

Photonic reagent control of dynamically homologous quantum systems

The general objective of quantum control is the manipulation of atomic scale physical and chemical phenomena through the application of external control fields. These tailored fields, or photonic reagents, exhibit systematic properties analogous to those of ordinary laboratory reagents. This analogous behavior is explored further here by considering the controlled response of a family of homologous quantum systems to a single common photonic reagent. A level set of dynamically homologous quantum systems is defined as the family that produces the same value(s) for a target physical observable(s) when controlled by a common photonic reagent. This paper investigates the scope of homologous quantum system control using the level set exploration technique (L-SET). L-SET enables the identification of continuous families of dynamically homologous quantum systems. Each quantum system is specified by a point in a hypercube whose edges are labeled by Hamiltonian matrix elements. Numerical examples are presented with simple finite level systems to illustrate the L-SET concepts. Both connected and disconnected families of dynamically homologous systems are shown to exist.     

Line-addressable digital-deflection programmable micromirror array

We report a novel digital-deflection programmable micromirror array driven by micromechanical digital-to-analog converters that eliminates the need for electrical digital-to-analog converters for analog displacement control, thus simplifying the driving circuitry and reducing the overall system cost. Furthermore, owing to the bistable and hysteretic characteristics of parallel-plate electrostatic actuators, an array of micromirrors can be controlled by means of row- and column-addressing lines, which drastically reduce the number of routing wires and allow array sizes to increase while they maintain high array quality.