Dynamical localization simulated on a few qubits quantum computer

We show that a quantum computer operating with a small number of qubits can simulate the dynamical localization of classical chaos in a system described by the quantum sawtooth map model. The dynamics of the system is computed efficiently up to a time $t\geq \ell$, and then the localization length $\ell$ can be obtained with accuracy $\nu$ by means of order $1/\nu^2$ computer runs, followed by coarse grained projective measurements on the computational basis. We also show that in the presence of static imperfections a reliable computation of the localization length is possible without error correction up to an imperfection threshold which drops polynomially with the number of qubits.