Mainz 2017 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 1: Quantum Information: Concepts and Methods I

Q 1.5: Vortrag

Montag, 6. März 2017, 16:00–16:15, P 2

Limits of Quantum Control: bounds on minimum time and control field amplitudes — •Christian Arenz, Benjamin Russell, and Herschel Rabitz — Frick Laboratory, Princeton University, Princeton NJ, 08544 US

We derive a lower bound for the time that is needed in order to implement a target unitary transformation through classical time-dependent fields. The bound depends on the target gate, the strength of the internal Hamiltonian and the highest control field amplitude. Furthermore, based on the established bound we characterize the reachable set of unitary operations as a function of the evolution time and the control field amplitude, here explicitly analyzed for a single qubit. Moreover, for a fully controllable system we show that the derived bound yields a lower bound for the time at which all unitary gates become reachable. We use numerical gate optimization in order to study the tightness of the obtained bounds. It is shown that in the single qubit case our analytical findings describe remarkably well the limit of reducing the highest control field amplitude and the evolution time as much as possible, while still being able to implement some unitary target operation. Finally we discuss the challenges in obtaining more accurate bounds for higher dimensional systems.