  We present a new technique for efficiently transitioning a quantum system
from an initial to a final stationary state in less time than is required by an
adiabatic (quasi-static) process. Our approach makes use of Nelson's stochastic
quantization, which represents the quantum system as a classical Brownian
process. Thanks to this mathematical analogy, known protocols for classical
overdamped systems can be translated into quantum protocols. In particular, one
can use classical methods to find optimal quantum protocols that minimize both
the time duration and some other cost function to be freely specified. We have
applied this method to the time-dependent harmonic oscillator and tested it on
two different cost functions: (i) the cumulative energy of the system over time
and (ii) the dynamical phase of the wavefunction. In the latter case, it is
possible to construct protocols that are "adiabatically optimal", i.e., they
minimize their distance from an adiabatic process for a given duration.
