  In adiabatic quantum computing finding the dependence of the gap of the
Hamiltonian as a function of the parameter varied during the adiabatic sweep is
crucial in order to optimize the speed of the computation. Inspired by this
challenge, in this work, we explore the potential of deep learning for
discovering a mapping from the parameters that fully identify a problem
Hamiltonian to the aforementioned parametric dependence of the gap applying
different network architectures. Through this example, we conjecture that a
limiting factor for the learnability of such problems is the size of the input,
that is, how the number of parameters needed to identify the Hamiltonian scales
with the system size. We show that a long short-term memory network succeeds in
predicting the gap when the parameter space scales linearly with system size.
Remarkably, we show that once this architecture is combined with a
convolutional neural network to deal with the spatial structure of the model,
the gap evolution can even be predicted for system sizes larger than the ones
seen by the neural network during training. This provides a significant speedup
in comparison with the existing exact and approximate algorithms in calculating
the gap.
