MATHQCI 2008 Madrid/Workshop

Speech's Title:
"Optimal Control in Quantum Spin Systems"

Harvard University
Division of Applied Sciences

Navin Khaneja's research lies in the area of control theory and its applications. He is currently working on developing methods for optimal control of quantum systems. These control techniques have been used for optimal pulse sequence design in high resolution nuclear magnetic resonance spectroscopy. The work also has applications to the areas of quantum information and computing. His recent work in the area of nonlinear control involves design of feedback controllers for stabilization of nonholonomic control systems. Professor Khaneja is also interested in problems of statistical inference. His work on Human Brain Mapping involved developing rich class of probabilistic models to capture inherent varaibility present in the anatomies and computationally efficient Bayesian inference algorithms for extracting anatomical information from noisy data collected through imaging modalities.

Selected Publications:

N. Khaneja and N.C. Nielsen "Triple oscillating field technique for accurate measurement of internuclear distances by solid state NMR spectroscopy" Journal of Chemical Physics (In Press).

N. Khaneja "Switched Control of Electron Nuclear Spin Systems " Phys. Rev. A , 76, 032326 (2007) .

H. Yuan, S.J. Glaser and N. Khaneja "Geodesics for efficient creation and propagation of order along Ising Spin Chains" Phys. Rev. A , 76, 012316 (2007) .

B. Pryor and N. Khaneja "Fourier decompositions and pulse sequence design algorithms for NMR in inhomogeneous fields " Journal of Chemical Physics, 125, 194111 (2006).

N. Khaneja, B. Heitmann, A. Spoerl, H. Yuan, T. Herbrueggen and S.J. Glaser, "Shortest paths for efficient control of indirectly coupled qubits", Phys. Rev. A, 75, 012322(2007) .

N. Khaneja "Sensitivity enhanced recoupling experiments in solid state NMR by gamma preparation" Journal of Magnetic Resonance 183, 261 (2006).

Haidong Yuan and N. Khaneja " Reachable set of bilinear control systems under time varying drift " System and control letters, 55, 501 (2006).

N. Khaneja, C. Kehlet, S.J. Glaser and N.C. Nielsen " Composite dipolar recoupling: Anisotropy compensated coherence transfer in solid-state nuclear magnetic resonance " Journal of Chemical Physics vol. 124, 114503 (2006).

J.S. Li and N. Khaneja " Control of inhomogeneous quantum ensembles" Phys. Rev. A. 73, 030302 (2006)

D. Frueh, T. Ito, J.S. Li, G. Wagner, S.J. Glaser, N. Khaneja " Sensitivity Enhancement in NMR of Macromolecules by application of Optimal Control Theory,"Journal of Biomolecular NMR vol. 32, no. 1, 23-30, (2005).

N. Khaneja, J.S. Li, C. Kehlet, B. Luy, S.J. Glaser " Broadband Relaxation Optimized Polarization Transfer in Magnetic Resonance,"Proceedings of National Academy of Sciences, USA vol. 101, 14742-14747, (2004).

N. Khaneja, B.Luy, S.J. Glaser " Boundary of Quantum Evolution under Decoherence,"Proceedings of National Academy of Sciences, USA vol. 100, no. 23, 13162-13166, (2003).

N. Khaneja, B. Luy, T. Reiss, S.J. Glaser " Optimal Control of Spin Dynamics in the Presence of Relaxation," Journal of Magnetic Resonance 162 : 311-319 (2003).

N. Khaneja and S.J. Glaser " Efficient transfer of coherence through Ising spin chains," Phys. Rev. A. 66, 060301(R) (2002).

N. Khaneja, S.J. Glaser and R.W. Brockett " Sub-Riemannian geometry and time optimal control of three spin systems: Coherence Transfer and Quantum Gates," Phys. Rev. A. 65: 032301 (2002).

N. Khaneja, R.W. Brockett and S.J. Glaser, " Time optimal control of spin systems," Phys. Rev. A. 63: 032308 (2001).

N. Khaneja and S.J. Glaser, "Cartan decomposition of SU(n) and Control of Spin Systems," Chem. Physics 267:11-23 (2001).

N. Khaneja and R.W. Brockett, " Dynamic Feedback Stabilization of Nonholonomic systems." Proceedings of Control and Dynamical Systems Conference. Phoenix AZ, 1640-45(1999).

N. Khaneja, M.I. Miller, and U. Grenander, " Dynamic Programming Generation of Curves on Brain Surfaces" IEEE Transactions on Pattern Analysis and Machine Intelligence.20:11 (1998).