Scientific
Research
My past scientific research can be subdivided into three categories:
- Quantum control and quantum estimation theory
- Optimization and computational complexity theory
- Biophysics
The unifying theme of all these areas is the framework of dynamical systems theory. My research is motivated by the observation that the mathematical tools of systems theory, which have been extensively developed in the context of classical physics, engineering control, and economics, can be applied with great success to the quantum and evolutionary biology realms as well.
Quantum control is the theory that underlies the development of the next generation of nanotechnologies that rely on quantum (rather than classical) effects for their function. This includes, but is not limited to, quantum computation. Classical control theory underlies essentially all modern technology, ranging from the embedded microelectronic controllers in devices such as cell phones and microcomputers, to the automation of nearly all major industrial plants in the world today.
We aim to extend these techniques to the quantum world. This involves, notably, debunking the myth that limitations on the observation of quantum systems renders their effective control difficult or impossible. Unlike most researchers in nanotechnology and quantum engineering, who focus on the development of specific device architectures or fabrication techniques - we develop the universal theory by which quantum dynamical systems can be engineered. This theory, and its affiliated numerical and experimental techniques, can be applied to any quantum system that may turn out to be the platform of choice in future quantum technologies. As such, we are in a position to collaborate fruitfully in this area with any experimental quantum engineers who are interested in optimizing the fidelity and robustness of their specific designs.
My work in biophysics focuses on evolutionary dynamics, which is an attempt to formulate the complex processes of natural selection in the language of the differential equations of physics. This involves both analytical theory and computational tools for biomolecular modeling and simulation. We and others have found that, in addition to providing a unified framework for understanding the processes of natural evolution, these techniques may allow us to design artificial biological systems - in particular, functional proteins - by mimicking the physical principles and selection strategies of nature at a vastly higher rate.
Computational protein engineering provides rational approach (to be distinguished from traditional blind combinatorial techniques) to biopharmaceutical drug design. Moreover, it may open the door to environmentally friendly alternative energy sources, such as next-generation biofuels.
My current research interests center on quantum control/estimation and theoretical (mathematical) biophysics. Although I plan to return to experimental biophysics in the future, I conduct my current research using primarily numerical and analytical tools. My research in optimization and complexity theory informs the design of algorithms and software by setting analytical bounds on the performance of numerical search strategies.
Please see the software and hardware development section for more details on some of the numerical tools that I use for this research. Please also see the table of contents for a new textbook I am now under contract to write on quantum control, entitled Quantum Control and Quantum Estimation Theory (Taylor & Francis publishing, scheduled for completion on Dec 31, 2009). The book's Preface is now also written. Writing of section 1 will pick up over the next several months, so stay tuned for updates.
Raj Chakrabarti
6/08