Preserving Quantum States using Inverting Pulses: A Super-Zeno Effect

We construct an algorithm for suppressing the transitions of a quantum mechanical system, initially prepared in a subspace $\mathcal{P}$ of the full Hilbert space of the system, to outside this subspace by subjecting it to a sequence of unequally spaced short-duration pulses. Each pulse multiplies the amplitude of the vectors in the subspace by $-1$. The number of pulses required by the algorithm to limit the leakage probability to $ϵ$ in time $T$ increases as $T\exp [\sqrt{\log (T^2/ϵ)}]$, compared to $T^2{ϵ}^{-1}$ in the standard quantum Zeno effect.

Figure 1

The plot of the upper bounds to the leakage probability vs the number of pulses. The curves are marked Z for the Zeno with periodic measurement, U for unitary evolution with periodic pulses, and S for the super-Zeno cases, for $ET=1$. Here $T$ is the total time for evolution, and $E$ is the norm of the Hamiltonian.