Minimum time optimal synthesis for two level quantum systems
- Dipartimento di Matematica, Università di Padova, Padova (Italy)
- Department of Mathematics, Iowa State University, Ames, Iowa 50011 (United States)
For the time optimal problem of an invariant system on SU(2), with two independent controls and a bound on the norm of the control, the extremals of the Pontryagin maximum principle are explicit functions of time. We use this fact here to perform the optimal synthesis for these systems, i.e., to find all time optimal trajectories. Although the Lie group SU(2) is three dimensional, time optimal trajectories can be described in the unit disk of the complex plane. We find that a circular trajectory separates optimal trajectories that reach the boundary of the unit disk from the others. Inside this separatrix circle, another trajectory (the critical trajectory) plays an important role in that all optimal trajectories end at an intersection with this curve. The results allow us to find the minimum time needed to achieve a given evolution of a two level quantum system.
- OSTI ID:
- 22403082
- Journal Information:
- Journal of Mathematical Physics, Vol. 56, Issue 1; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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