Time-optimal control of finite quantum systems

We investigate time-optimal control of finite quantum systems in the Born approximation. A bang–bang principle is found to follow from a result in [C. A. Akemann and J. Anderson, Mem. Amer. Math. Soc. 458 (1991)]. We also prove existence of time-optimal controls, characterize when they are unique, and assuming uniqueness, explicitly describe them.

[1]  Nik Weaver.  On the universality of almost every quantum logic gate , 2000 .

[2]  H. Helson.  Harmonic Analysis , 1983 .

[3]  H. Rabitz,et al.  Teaching lasers to control molecules. , 1992, Physical review letters.

[4]  H. Sussmann,et al.  Control systems on Lie groups , 1972 .

[5]  Günter Mahler,et al.  Nanostructures, Entanglement and the Physics of Quantum Control , 1994 .

[6]  K. Kime,et al.  Control of transition probabilities of the quantum-mechanical harmonic oscillator , 1993 .

[7]  Ramakrishna,et al.  Controllability of molecular systems. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[8]  A. G. Butkovskii,et al.  Control of Quantum-Mechanical Processes and Systems , 1990 .

[9]  R. Kadison,et al.  Fundamentals of the Theory of Operator Algebras , 1983 .

[10]  H. Rabitz,et al.  Optimal control of quantum-mechanical systems: Existence, numerical approximation, and applications. , 1988, Physical review. A, General physics.

[11]  Ramakrishna,et al.  Relation between quantum computing and quantum controllability. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[12]  Lloyd,et al.  Almost any quantum logic gate is universal. , 1995, Physical review letters.

[13]  Herschel Rabitz,et al.  Coherent Control of Quantum Dynamics: The Dream Is Alive , 1993, Science.

[14]  T. Tarn,et al.  On the controllability of quantum‐mechanical systems , 1983 .

[15]  J. P. Lasalle,et al.  functional analysis and time Optimal Control , 1969 .

[16]  A. Boukas.  Application of quantum stochastic calculus to optimal control , 1993 .

[17]  Wiseman,et al.  Quantum theory of continuous feedback. , 1994, Physical review. A, Atomic, molecular, and optical physics.