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.
@article{arxiv.1905.06728,
title = {Implementing perceptron models with qubits},
author = {Roeland Wiersema and H. J. Kappen},
journal= {arXiv preprint arXiv:1905.06728},
year = {2023}
}