Complexity of controlling quantum many-body dynamics.

We demonstrate that arbitrary time evolutions of many-body quantum systems can be reversed even in cases when only part of the Hamiltonian can be controlled. The reversed dynamics obtained via optimal control-- contrary to standard time-reversal procedures--is extremely robust to external sources of noise. We provide a lower bound on the control complexity of a many-body quantum dynamics in terms of the dimension of the manifold supporting it, elucidating the role played by integrability in this context. [ABSTRACT FROM AUTHOR]