  We propose a method for learning a quantum probabilistic model of a
perceptron. By considering a cross entropy between two density matrices we can
learn a model that takes noisy output labels into account while learning. A
multitude of proposals already exist that aim to utilize the curious properties
of quantum systems to build a quantum perceptron, but these proposals rely on a
classical cost function for the optimization procedure. We demonstrate the
usage of a quantum equivalent of the classical log-likelihood, which allows for
a quantum model and training procedure. We show that this allows us to better
capture noisyness in data compared to a classical perceptron. By considering
entangled qubits we can learn nonlinear separation boundaries, such as XOR.
