Classification of data with a qudit, a geometric approach

TL;DR

This paper introduces a geometric quantum model using qudits for data classification, encoding classical data on a Bloch hyper-sphere, and optimizing rotations and weights through gradient descent to solve nonlinear problems efficiently.

Contribution

It presents a novel geometric approach for qudit-based classification that avoids entanglement and uses minimal parameters, expanding quantum machine learning methods.

Findings

Successfully classifies nonlinear data with few parameters

Demonstrates the model's capability through numerical experiments

Shows the model does not require entangling operations

Abstract

We propose a model for data classification using isolated quantum $d$-level systems or else qudits. The procedure consists of an encoding phase where classical data are mapped on the surface of the qudit's Bloch hyper-sphere via rotation encoding, followed by a rotation of the sphere and a projective measurement. The rotation is adjustable in order to control the operator to be measured, while additional weights are introduced in the encoding phase adjusting the mapping on the Bloch's hyper-surface. During the training phase, a cost function based on the average expectation value of the observable is minimized using gradient descent thereby adjusting the weights. Using examples and performing a numerical estimation of lossless memory dimension, we demonstrate that this geometrically inspired qudit model for classification is able to solve nonlinear classification problems using a small number of parameters only and without requiring entangling operations.