Evening Special Talk Room1, 16:30-17:30, September 17, 2007
Control of Decoherence in Open Quantum Systems Using Feedback:
Quantum Internal Model Principle
Professor T.J. Tarn
Washington University and Tsinghua University
Decoherence, which is caused due to the interaction of a quantum system with its environment plagues all quantum systems and leads to the loss of quantum properties that are vital for quantum computation and quantum information processing. In this work we propose a novel strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done so. A novel construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment, is presented. This corresponds to the Internal Model Principle for Quantum Mechanical Systems. Almost all the earlier work on decoherence control employ density matrix and stochastic master equations to analyze the problem.
Our approach to decoherence control involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with non-trivial modifications to the quantum regime. The elegance of this approach yields interesting results on open loop decouplability and Decoherence Free Subspaces (DFS). Additionally, the feedback control of decoherence may be related to disturbance decoupling for classical input affine systems, which entails careful application of the methods by avoiding all the quantum mechanical pitfalls. The two concepts are contrasted and an improved theory of disturbance decoupling for general input affine systems is developed. In the process of calculating a suitable feedback the system has to be restructured due to its tensorial nature of interaction with the environment, which is unique to quantum systems. Finally the results are also shown to be superior to the ones obtained via master equations. In order to apply feedback a reliable information extraction scheme using continuous indirect measurements with the help of a quantum probe is outlined. Finally, a methodology to synthesize feedback parameters itself is given, that technology permitting, could be implemented for practical 2-qubit systems to perform decoherence free Quantum Computing.

T.J. Tarn, Ph.D., professor of Systems Science and Mathematics in the School of Engineering and Applied Science, is internationally known for his expertise in robotics and automation and intelligent control. In 1997, Tarn and his then graduate student Kevin Brady were the first persons to control a robot live via the Internet. The "teleoperations" feat was a major step for the burgeoning field of robotics and a giant leap for telecommunications, adding a previously unexplored dimension to the Internet - remote control - and providing new horizons for other applications. In accomplishing this, Tarn showed that the Internet could be a medium to transfer force, rather than strictly a communications system, which is the way it had been seen. In 1998, sensing, or gathering, with high-level planning and decision-making processes. The theory, encapsulated in an algorithm, completely automates the process whereby a system must adapt to changing conditions. Building on these advances, Tarn tuned to synchronizing and integrating scheduling, planning and control for underwater robotics vehicles in a project sponsored by the National Science Foundation. Tarn has been awarded the title of Honorary Professor at several Chinese universities, including Chengdu University of Science and Technology and Tsinghua University. In 1993, he was general chairman of the First World Congress on Intelligent Control and Intelligent Automation, in Beijing, China