What is the physical nature of information? Recent research has shown that the answer is profoundly connected to quantum theory. Information is physical and can exist in superpositions, or become entangled. These are unique quantum features, which make the study of quantum information much more interesting and challenging then classical information.
My research interests are primarily in the related field of quantum information processing. The ultimate information processor is a quantum computer: a computer that uses quantum bits ("qubits") and quantum circuitry to perform calculations. Quantum computers can tackle problems that would stymie their conventional (i.e., classical) counterparts. For instance, cracking the most sophisticated encryption schemes, performing many-body correlated-electrons simulations, or searching large random lists. Small quantum computers can act as nodes in a perfectly secure quantum communications network. These applications, and many others, have led to an explosive multidisciplinary effort to understand what it would take to build quantum computers.
The toughest problem is the process of decoherence. This is the result of the interaction of a quantum system with its environment. The environment "measures" the system and collapses superpositions. A quantum computer must be protected from decoherence, since this process introduces computational errors and causes a slowdown to classical speeds. One project I am very interested in is the design of "quantum error correction" methods that circumvent the decoherence problem.
Another fundamental problem is to identify the optimal physical system to serve as a quantum computer. Many proposals have been made, some have even been implemented experimentally on a very small scale (e.g., NMR), but so far it is unclear if these implementations can be scaled up to construct a truly useful quantum computer. A very promising architecture are quantum dots: artificially patterned semiconductors that confine electrons in three spatial dimensions on a nanometer scale. Each confined electron can serve as a qubit, with the quantum information encoded into the electron spin, position, or energy level. A second project of great interest to me is the study of quantum dots as a medium to implement quantum computers. Quantum dots may not be optimal either, however, and I am considering other media as well.
A third major research interest of mine is the extension of the theory of quantum control to deal with open quantum systems. Contrary to the popular textbook view, quantum systems are not closed, since any real system interacts with its environment in some uncontrollable way (and thus decoheres). Quantum control aims to steer a quantum system along a desired trajectory, e.g., in order to optimize the yield of a chemical reaction, or to process information. While quantum control theory is well developed for closed systems (governed by the Schrodinger equation), very little is known about quantum control in the presence of decoherence and noise. This is a fascinating open field, with many potential applications.