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Motivation

Systematic study of quantum systems through modelling, simulations and experiments is crucial for advancing our understanding of quantum phenomena. Significant recent progress in many areas from nanoengineering to laser technology have greatly contributed to make quantum phenomena accessible and even controllable through coherent control, controlled measurements and feedback. Although engineering the Hamiltonian or the interaction of a system with an external environment are no simple tasks, the ability to control the properties and dynamic behaviour of quantum systems is essential for the development of new technologies exploiting quantum effects such as coherence and entanglement. The applications of such new technologies are wide-ranging from control of chemical reactions to laser cooling to quantum metrology and quantum computing.

Publications & Preprints

Accessible Reviews etc Quantum Choreography: Making Molecules Dance to Technology's Tune?, SG Schirmer, Triennial Issue of Phil. Trans. R. Soc. A364, 3423 (2006) Control Paradigms for Quantum Engineering, SG Schirmer, G Kandasamy, SJ Devitt, IEEE Proc ISCCSP08, 966 (2008) Physics-based mathematical models for quantum devices via experimental system identification, SG Schirmer, DKL Oi, SJ Devitt, J. Phys.: Conf. Series107, 012011 (2008) (Workshop on Physics-based Models of Low-Dimensional Semiconductor Nanostructures, Banff Int'l Research Station, Canada) Video of a talk on Hamiltonian and Markovian Reservoir Engineering (IMA, Minnesota, 2009) Quantum Modelling & System Identification High-Q photonic crystal cavity with truncated cone air holes, F Brossard, SG Schirmer, DA Williams, to be submitted to APL Hamiltonian Tomography for Two-Qubit System using Baysean Analysis of Noisy Data, SG Schirmer, DKL Oi, arXiv:0902.3434, submitted to Phys. Rev. On the identifiability of model parameters of quantum systems, Ming Zhang, SG Schirmer, submitted to CDC 2009 Intrinsic characterization protocols for qubit systems, SJ Devitt, JH Cole, SG Schirmer, DKL Oi, LCL Hollenberg, Proc. ICONN08 (2008) Subspace Confinement: How good is your qubit?, SJ Devitt, SG Schirmer, DKL Oi, JH Cole, LCL Hollenberg, New Journal of Physics 9, 384 (2007) Research Highlights: Qubit quality quantified, SJ Devitt, SG Schirmer, DKL Oi, JH Cole, LCL Hollenberg, Nature Physics 797(3), 830 (2007) Identifying a two-state Hamiltonian in the presence of decoherence, JH Cole, AD Greentree, DKL Oi, SG Schirmer, CJ Wellard, LCL Hollenberg, Phys. Rev. A 73, 062333 (2006); Virtual Journal of Quantum Information (July 2006). Identifying an experimental two-state Hamiltonian to arbitary accuracy, JH Cole, SG Schirmer, AD Greentree, CJ Wellard, DKL Oi, LCL Hollenberg, Phys. Rev. A 71, 062312 (2005); Virtual Journal of Quantum Information (June 2005). Experimental Hamiltonian identification for qubits subject to multiple independent control mechanisms, S. G. Schirmer, A. Kolli, D. K. L. Oi, J. H. Cole, Proc of QCMC04 (AIP 2004) Experimental Hamiltonian identification for controlled two-level systems, SG Schirmer, A Kolli, DKL Oi, Phys. Rev. A 69, 050306 (2004); Virtual Journal of Quantum Information (June 2004) Controllability, Reachable States, Limits on Control Global controllability with a single local actuator, SG Schirmer, ICH Pullen, PJ Pemberton-Ross, Phys. Rev. A 78, 062339 (2008); Virtual J. Nanoscience & Technology (Jan 12, 2009) Controllability of multi-partite quantum systems and selective excitation of quantum dots, SG Schirmer, ICH Pullen, AI Solomon, J. Opt. B 7, S293-S299 (2005); Special Issue on Quantum Control. Controllability of Quantum Systems, SG Schirmer, ICH Pullen, AI Solomon, in Hamiltonian and Lagrangian Methods in Nonlinear Control (ISBN 0-08-044278-1) 2003 Criteria for reachability of states for quantum systems, SG Schirmer, JV Leahy, AI Solomon, J. Phys. A 35, 8551-8562 (2002) Limitations on quantum control, AI Solomon, SG Schirmer, Int. J. Mod. Phys. B 16, 2107-2112 (2002) Degrees of controllability for quantum systems and application to atomic systems, SG Schirmer, JV Leahy, AI Solomon, J. Phys. A 35, 4125-4141 (2002) Complete controllability of finite-level quantum systems, H Fu, SG Schirmer, AI Solomon, J. Phys. A 34, 1679-1693 (2001) Complete controllability of quantum systems, SG Schirmer, H Fu and AI Solomon, Phys. Rev. A 63, 063410 (2001) Limits of control for quantum systems: kinematical bounds on the optimization of observables and the question of dynamical realizability, SG Schirmer, JV Leahy, Phys. Rev. A 63, 025403 (2001) Non-reachable target states for pure-state controllable and non-controllable quantum systems, SG Schirmer, AI Solomon, in 40th IEEE CDC Proceedings (ISBN 0-7803-7063-5), 2605-2606 (2001) Dynamical realizability of kinematical bounds on the optimization of observables for quantum systems, JV Leahy, SG Schirmer, in 39th IEEE CDC Proceedings (ISBN 0-7803-6641-7), 1358-1363 (2000) Kinematical bounds on the optimization of observables for quantum systems, the question of their dynamical realizability and Lie groups, SG Schirmer, H Fu, AI Solomon, in Proceedings 23rd Colloquium on Group Theoretical Methods in Physics (Dubna, Russia, 2000) Kinematical bounds on optimization of observables for quantum systems, MD Girardeau, SG Schirmer, JV Leahy, RM Koch, Phys. Rev. A 58, 2684-2689 (1998) Kinematical bounds on evolution and optimization of mixed quantum states, MD Girardeau, M Ina, SG Schirmer, T Gulsrud, Phys. Rev. A 55, R1565-R1568 (1997) Coherent Control & Applications Optimal Control Algorithms for Quantum Systems and their Limitations, SG Schirmer, PL Becq de Fouquieres, X Wang, submitted to PhysCon09 Fast high-fidelity information transfer in spin chain quantum wires, SG Schirmer, PJ Pemberton-Ross, submitted to Phys. Rev. Analysis of Lyapunov method for control of quantum states: generic case, X Wang, SG Schirmer, submitted to IEEE TAC, 2008 Analysis of Lyapunov method for control of quantum states: nongeneric case. X Wang, SG Schirmer, submitted to IEEE TAC, 2008 Implementation of quantum gates via optimal control, SG Schirmer, J. Mod. Optics 2009, 1-9. (special issue on quantum control, online version = preprint) Explicit algorithm for generalized Euler angle decomposition of SU(2), KCh Chatzisavvas, C Daskaloyannis, CP Panos, SG Schirmer. Analysis of Lyapunov Control of Hamiltonian Quantum Systems, X Wang, SG Schirmer, in Proc ENOC08 (St Petersburg, Russia, 2008) Hamiltonian engineering for quantum systems, SG Schirmer, in Proc 3rd IFAC Workshop on Lagragian and Hamiltonian Methods in Nonlinear Control (Nagoya, Japan, July 2006) Robust charge-based qubit encoding, DKL Oi, SG Schirmer, AD Greentree, TM Stace, Phys. Rev. B 72, 075348 (2005); Virtual Journal of Nanoscale Science & Technology (Sep 5, 2005) Controlled phase gate for solid-state charge-qubit architectures, SG Schirmer, DKL Oi, AD Greentree, Phys. Rev. A 71, 012325 (2005); Virtual Journal of Quantum Information (Feb 2005); Virtual Journal of Nanoscale Science and Technology (Jan 31, 2005) Quantum control using sequences of simple control pulses, SG Schirmer, AD Greentree, V Ramakrishna, H Rabitz, J. Phys. A 35, 8315-8339 (2002) Geometric control for atomic systems, SG Schirmer, in Proceedings SIAM Conf. Mathematical Theory of Systems and Networks (South Bend, IN, 2002), www.nd.edu/~mtns/papers/20270_3.pdf. Quantum control of dissipative systems, SG Schirmer, in Proceedings SIAM Conf. Mathematical Theory of Systems and Networks (South Bend, IN, 2002), see also www.nd.edu/~mtns/papers/2178_4.pdf. Laser cooling of internal molecular degrees of freedom for vibrationally hot molecules, SG Schirmer, Phys. Rev. A 63, 013407 (2001) Quantum control using Lie group decompositions, SG Schirmer, 40th IEEE CDC Proceedings (ISBN 0-7803-7063-5), 298-303 (2001) Group-theoretical aspects of control of quantum systems, SG Schirmer, AI Solomon, in Proceedings 2nd Int'l Symposium on Quantum Theory and Symmetries (Cracow, Poland, July 2001) Control of population inversion in presence of spontaneous emission, SG Schirmer, AD Greentree, AV Durrant, in Proceedings 8th Rochester Conf. Quantum Coherence (Rochester, NY, 2001) Robust quantum memory using quantum control, AD Greentree, SG Schirmer, AI Solomon, Proceedings 1st Int'l Conf. Quantum Information (Rochester, NY, 2001) Efficient algorithm for optimal control of mixed-state quantum systems, SG Schirmer, MD Girardeau, JV Leahy, Phys. Rev. A 61, 012101 (2000) Laser cooling of internal molecular degrees of freedom, SG Schirmer, in 39th IEEE CDC Proceedings (ISBN 0-7803-6641-7), 1376-1381 (2000) General Quantum Physics, Decoherence, etc. On the Contractivity of Trace-preserving Quantum Operations, X Wang, SG Schirmer, arXiv:0901.4547, submitted to Phys. Rev. Bohm-Aharanov type effects in dissipative atomic systems, AI Solomon, SG Schirmer, quant-ph/0512198, Proc 23rd Int'l Conf. Differential Geometric Methods in Theoretical Physics (Nankai, China, Aug 20-26, 2005) Constraints on relaxation rates for N-level quantum systems, SG Schirmer, AI Solomon, Phys. Rev. A 70, 022107 (2004) Maximizing the Hilbert space for a finite number of distinguishable quantum states, AD Greentree, SG Schirmer, F Green, LCL Hollenberg, AR Hamilton, RC Clark, Phys. Rev. Lett., 92, 097901 (2004); Virtual Journal of Quantum Information (March 2004); Virtual Journal of Nanoscale Science and Technology (March 15, 2004) Orbits of quantum states and geometry of Bloch vectors for N-level systems, SG Schirmer, T Zhang, JV Leahy, J. Phys. A 37, 1389 (2004) Dissipative Groups and the Bloch Ball AI Solomon, SG Schirmer, in Group 24: Physical and Mathematical Aspects of Symmetries (ISBN 0-75-030933-4) 2003