# Implementing perceptron models with qubits

## TL;DR

This paper introduces a quantum perceptron model that uses a quantum cross-entropy loss function, enabling better handling of noisy data and nonlinear decision boundaries like XOR.

## Contribution

It presents a novel quantum training method based on a quantum log-likelihood, improving noise robustness and nonlinear separability in quantum perceptrons.

## Key findings

- Quantum cross-entropy effectively models noisy data.
- The quantum perceptron can learn nonlinear boundaries like XOR.
- Enhanced noise handling compared to classical perceptrons.

## Abstract

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.