  Inspired by the success of Boltzmann Machines based on classical Boltzmann
distribution, we propose a new machine learning approach based on quantum
Boltzmann distribution of a transverse-field Ising Hamiltonian. Due to the
non-commutative nature of quantum mechanics, the training process of the
Quantum Boltzmann Machine (QBM) can become nontrivial. We circumvent the
problem by introducing bounds on the quantum probabilities. This allows us to
train the QBM efficiently by sampling. We show examples of QBM training with
and without the bound, using exact diagonalization, and compare the results
with classical Boltzmann training. We also discuss the possibility of using
quantum annealing processors like D-Wave for QBM training and application.
