Qudit Machine Learning

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.

19 pages, 11 figures

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Cited by in corpus (8)

• Quantum Machine Learning in Drug Discovery: Applications in Academia and Pharmaceutical Industries
• Artificial Intelligence for Quantum Computing
• Variational Quantum Multi-Objective Optimization
• Satellite image classification with neural quantum kernels
• QuForge: A Library for Qudits Simulation
• Inequality constraints in variational quantum circuits with qudits
• Barren plateaus are amplified by the dimension of qudits
• A genetic algorithm to generate maximally orthogonal frames in complex space