  Quantum machine learning has emerged as a potential practical application of
near-term quantum devices. In this work, we study a two-layer hybrid
classical-quantum classifier in which a first layer of quantum stochastic
neurons implementing generalized linear models (QGLMs) is followed by a second
classical combining layer. The input to the first, hidden, layer is obtained
via amplitude encoding in order to leverage the exponential size of the fan-in
of the quantum neurons in the number of qubits per neuron. To facilitate
implementation of the QGLMs, all weights and activations are binary. While the
state of the art on training strategies for this class of models is limited to
exhaustive search and single-neuron perceptron-like bit-flip strategies, this
letter introduces a stochastic variational optimization approach that enables
the joint training of quantum and classical layers via stochastic gradient
descent. Experiments show the advantages of the approach for a variety of
activation functions implemented by QGLM neurons.
