Zeno effect for quantum computation and control.

It is well known that the quantum Zeno effect can protect specific quantum states from decoherence by using projective measurements. Here we combine the theory of weak measurements with stabilizer quantum error correction and detection codes. We derive rigorous performance bounds which demonstrate that the Zeno effect can be used to protect appropriately encoded arbitrary states to arbitrary accuracy while at the same time allowing for universal quantum computation or quantum control.

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.

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.

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.