  Near term quantum hardware promises to achieve quantum supremacy. From a
quantum dynamical point of view, however, it is not unambiguously clear whether
fundamental peculiarities of quantum physics permit any arbitrary speed-ups in
real time. We show that an only recently unveiled property of the quantum
Fisher information has profound implications for the rate of possible quantum
information processing. To this end, we analyze an exemplary and pedagogical
example for a quantum computer consisting of a computational qubit and a
quantum memory. We find that frequent interaction between memory and device
exhibit the quantum Zeno effect. In a second part, we show that the Zeno effect
can be prevented by carefully designing the correlations and interaction
between single elements of the quantum memory.
