Time optimal simultaneous control of two level quantum systems

Automatica - Tập 74 - Trang 55-62 - 2016
Francesca Albertini1, Domenico D’Alessandro2
1Dipartimento di Tecnica e Gestione dei Sistemi Industriali, Università di Padova, Italy
2Department of Mathematics, Iowa State University, Ames, IA, USA

Tài liệu tham khảo

Abragam, 2002, Vol. 32 Aiello, 2015, Algebraic synthesis of time-optimal unitaries in SU(2) with alternating controls, Quantum Information Processing, 14, 3233173256, 10.1007/s11128-015-1045-6 Albertini, 2015, Minimum time optimal synthesis for two level quantum systems, Journal of Mathematical Physics, 56, 10.1063/1.4906137 Albertini, F., & D’Alessandro, D. (2016). http://www.public.iastate.edu/~daless/appendix-A.pdf. Beauchard, 2012, Stabilization for an ensemble of half-spin systems, Automatica, 48, 10.1016/j.automatica.2011.09.050 Billig, Y. (2014). Optimal attitude control with two rotation axes, arXiv:1409.3102. Billig, 2013, Time-optimal decompositions in SU(2), Quantum Information Processing, 12, 955, 10.1007/s11128-012-0447-y Boscain, 2002, On the K+P problem for a three-level quantum system: Optimality implies resonance, Journal of Dynamical and Control Systems, 8, 547, 10.1023/A:1020767419671 Boscain, 2014, Minimal time trajectories for two-level quantum systems with two bounded controls, Journal of Mathematical Physics, 55, 10.1063/1.4882158 Boscain, 2006, Time minimal trajectories for a spin 12 particle in a magnetic field, Journal of Mathematical Physics, 47, 10.1063/1.2203236 Boscain, 2004, Vol. 43 Boscain, 2008, Invariant Carnot-Caratheodory metric on S3, SO(3) and SL(2) and lens spaces, SIAM Journal on Control and Optimization, 47, 1851, 10.1137/070703727 Carlini, 2006, Time optimal quantum evolution, Physical Review Letters, 96, 10.1103/PhysRevLett.96.060503 Carlini, 2007, Time optimal unitary evolutions, Phys. Rev. A, 75, 10.1103/PhysRevA.75.042308 Chen, 2014, Sampling-based learning control of inhomogeneous quantum ensembles, Physical Review A, 89, 10.1103/PhysRevA.89.023402 D’Alessandro, 2007 D’Alessandro, 2004, Optimal evaluation of generalized Euler angles with applications to control, Automatica, 40, 1997, 10.1016/j.automatica.2004.06.006 D’Alessandro, 2001, Otimal control of two-level quantum systems, IEEE Transactions on Automatic Control, 45 Khaneja, 2001, Time optimal control of spin systems, Phys. Rev. A, 63, 10.1103/PhysRevA.63.032308 Li, 2009, Ensemble control of Bloch equations, IEEE Transactions on Automatic Control, 54, 52817536, 10.1109/TAC.2009.2012983 Mazzarella, 2015, Consensus for quantum networks: From symmetry to gossip iterations, IEEE Transactions on Automatic Control, 60, 158, 10.1109/TAC.2014.2336351 Nielsen, 2000 Ohsawa, 2013, Symmetry reduction of optimal control systems and principal connections, SIAM Journal on Control and Optimization, 51, 96, 10.1137/110835219 Romano, 2014, Geometric analysis of minimum time trajectories for a two level quantum system, Physical Review A, 90, 10.1103/PhysRevA.90.062302 Sakurai, 1994 Shi, 2015, Reaching a quantum consensus: Master equations that generate symmetrization and synchronization, IEEE Transactions on Automatic Control, 10.1109/TAC.2015.2434034 Wang, 2015, Quantum brachistochrone curves as geodesics: obtaining accurate control protocols for time-optimal quantum gates, Physical Review Letters, 114, 10.1103/PhysRevLett.114.170501