  Quantum information-processing techniques enable work extraction from a
system's inherently quantum features, in addition to the classical free energy
it contains. Meanwhile, the science of computational mechanics affords tools
for the predictive modeling of non-Markovian classical and quantum stochastic
processes. We combine tools from these two sciences to develop a technique for
predictive work extraction from non-Markovian stochastic processes with quantum
outputs. We demonstrate that this technique can extract more work than
non-predictive quantum work extraction protocols, on one hand, and predictive
work extraction without quantum information processing, on the other. We
discover a phase transition in the efficacy of memory for work extraction from
quantum processes, which is without classical precedent. Our work opens up the
prospect of machines that harness environmental free energy in an essentially
quantum, essentially time-varying form.
