  Ising machines, which are hardware implementations of the Ising model of
coupled spins, have been influential in the development of unsupervised
learning algorithms at the origins of Artificial Intelligence (AI). However,
their application to AI has been limited due to the complexities in matching
supervised training methods with Ising machine physics, even though these
methods are essential for achieving high accuracy. In this study, we
demonstrate a novel approach to train Ising machines in a supervised way
through the Equilibrium Propagation algorithm, achieving comparable results to
software-based implementations. We employ the quantum annealing procedure of
the D-Wave Ising machine to train a fully-connected neural network on the MNIST
dataset. Furthermore, we demonstrate that the machine's connectivity supports
convolution operations, enabling the training of a compact convolutional
network with minimal spins per neuron. Our findings establish Ising machines as
a promising trainable hardware platform for AI, with the potential to enhance
machine learning applications.
