  The goal of this work is to define a notion of a quantum neural network to
classify data, which exploits the low energy spectrum of a local Hamiltonian.
As a concrete application, we build a binary classifier, train it on some
actual data and then test its performance on a simple classification task. More
specifically, we use Microsoft's quantum simulator, Liquid, to construct local
Hamiltonians that can encode trained classifier functions in their ground
space, and which can be probed by measuring the overlap with test states
corresponding to the data to be classified. To obtain such a classifier
Hamiltonian, we further propose a training scheme based on quantum annealing
which is completely closed-off to the environment and which does not depend on
external measurements until the very end, avoiding unnecessary decoherence
during the annealing procedure. For a network of size n, the trained network
can be stored as a list of O(n) coupling strengths. We address the question of
which interactions are most suitable for a given classification task, and
develop a qubit-saving optimization for the training procedure on a simulated
annealing device. Furthermore, a small neural network to classify colors into
red vs. blue is trained and tested, and benchmarked against the annealing
parameters.
