  We explore the question as to whether quantum effects can yield a speedup of
the non-equilibrium evolution of spin systems towards a classical thermal
state. In our approach we exploit the fact that the thermal state of a spin
system can be mapped onto a node-free quantum state whose coefficients are
given by thermal weights. This perspective permits the construction of a
dissipative -- yet quantum -- dynamics which encodes in its stationary state
the thermal state of the original problem. We show for the case of an
all-to-all connected Ising spin model that an appropriate transformation of
this dissipative dynamics allows to interpolate between a regime in which the
order parameter obeys the classical equations of motion under Glauber dynamics,
to a quantum regime with an accelerated approach to stationarity. We show that
this effect enables in principle a speedup of pattern retrieval in a Hopfield
neural network.
