  We extend the concept of Anderson localization, the confinement of quantum
information in a spatially irregular potential, to quantum circuits.
Considering matchgate circuits, generated by time-dependent spin-1/2 XY
Hamiltonians, we give an analytic formula for the out-of-time-ordered
correlator of a local observable, and show that it can be efficiently evaluated
by a classical computer even when the explicit Heisenberg time evolution
cannot. Because this quantity bounds the average error incurred by truncating
the evolution to a spatially limited region, we demonstrate dynamical
localization as a means for classically simulating quantum computation and give
examples of localized phases under certain spatio-temporal disordered
Hamiltonians.
