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, LIQ[Formula: see text][Formula: see text], 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 [Formula: see text], the trained network can be stored as a list of [Formula: see text] 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 versus blue is trained and tested, and benchmarked against the annealing parameters.
Moiré heterostructures as a condensed-matter quantum simulator
