Qudit Machine Learning

TL;DR

This paper investigates the use of qudits for machine learning classification tasks, demonstrating that small quantum systems can outperform classical models on low-dimensional data but face limitations with high-dimensional datasets like MNIST.

Contribution

It introduces a comprehensive framework for qudit-based learning, exploring encoding strategies and showing conditions where quantum models excel or are limited.

Findings

Quantum models outperform classical ones on low-dimensional data when feature and class counts are small.

Small quantum systems face accuracy bottlenecks with high-dimensional data like MNIST.

Hybrid classical-quantum approaches can mitigate some limitations of quantum models.

Abstract

We present a comprehensive investigation into the learning capabilities of a simple d-level system (qudit). Our study is specialized for classification tasks using real-world databases, specifically the Iris, breast cancer, and MNIST datasets. We explore various learning models in the metric learning framework, along with different encoding strategies. In particular, we employ data re-uploading techniques and maximally orthogonal states to accommodate input data within low-dimensional systems. Our findings reveal optimal strategies, indicating that when the dimension of input feature data and the number of classes are not significantly larger than the qudit's dimension, our results show favorable comparisons against the best classical models. This trend holds true even for small quantum systems, with dimensions d<5 and utilizing algorithms with a few layers (L=1,2). However, for high-dimensional data such as MNIST, we adopt a hybrid approach involving dimensional reduction through a convolutional neural network. In this context, we observe that small quantum systems often act as bottlenecks, resulting in lower accuracy compared to their classical counterparts.