Figure 1: Zeno effect in quantum control.

(a) We control a quantum system by switching on and off a set of given Hamiltonians {H⁽¹⁾,…, H⁽ⁿ⁾}. (b) We perform projective measurements P at regular time intervals during the control to check whether or not the state of the system belongs to a given subspace of the global Hilbert space. (c) In the limit of infinitely frequent measurements (Zeno limit), the system is confined in the subspace , where it evolves unitarily with the Zeno Hamiltonians {⁽¹⁾,..., ⁽ⁿ⁾} (Zeno dynamics). The Zeno dynamics can explore the subspace more thoroughly than the purely unitary control without measurement.