Incoherent Control of Locally Controllable Quantum Systems

Details Incoherent Control of Locally Controllable Quantum Systems Incoherent Control of Locally Controllable Quantum Systems

2008-10-21

arxiv.org/abs/0810.3814v1

Journal of Chemical Physics, Vol.129, p.154103, 2008

Physics

Quantum Physics

25 pages, 5 figures, Latex

Scientific paper

10.1063/1.2992557

An incoherent control scheme for state control of locally controllable quantum systems is proposed. This scheme includes three steps: (1) amplitude amplification of the initial state by a suitable unitary transformation, (2) projective measurement on the amplified state, and (3) final optimization by a unitary controlled transformation. The first step increases the amplitudes of some desired eigenstates and the corresponding probability of observing these eigenstates, the second step projects, with high probability, the amplified state into a desired eigenstate, and the last step steers this eigenstate into the target state. Within this scheme, two control algorithms are presented for two classes of quantum systems. As an example, the incoherent control scheme is applied to the control of a hydrogen atom by an external field. The results support the suggestion that projective measurements can serve as an effective control and local controllability information can be used to design control laws for quantum systems. Thus, this scheme establishes a subtle connection between control design and controllability analysis of quantum systems and provides an effective engineering approach for controlling quantum systems with partial controllability information.

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