Implementing perceptron models with qubits

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. Although some work has been done that aims to utilize the curious properties of quantum systems to build a quantum perceptron, these proposals rely on the ad hoc introduction of a classical cost functionfor the optimization procedure. We demonstrate the usage of a quantum probabilistic model by considering a quantum equivalent of the classical log-likelihood, which allows for both 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.