Single-Qudit Quantum Neural Networks for Multiclass Classification

Abstract

This paper proposes a single-qudit quantum neural network for multiclass classification, by using the enhanced representational capacity of high-dimensional qudit states. Our design employs an $d$-dimensional unitary operator, where $d$ corresponds to the number of classes, constructed using the Cayley transform of a skew-symmetric matrix, to efficiently encode and process class information. This architecture enables a direct mapping between class labels and quantum measurement outcomes, reducing circuit depth and computational overhead. To optimize network parameters, we introduce a hybrid training approach that combines an extended activation function -- derived from a truncated multivariable Taylor series expansion -- with support vector machine optimization for weight determination. We evaluate our model on the MNIST and EMNIST datasets, demonstrating competitive accuracy while maintaining a compact single-qudit quantum circuit. Our findings highlight the potential of qudit-based QNNs as scalable alternatives to classical deep learning models, particularly for multiclass classification. However, practical implementation remains constrained by current quantum hardware limitations. This research advances quantum machine learning by demonstrating the feasibility of higher-dimensional quantum systems for efficient learning tasks.

24 pages, 3 figures, 6 tables

References in corpus (24)

• The effect of data encoding on the expressive power of variational quantum machine learning models
• Power of data in quantum machine learning
• The quest for a Quantum Neural Network
• Qudits and high-dimensional quantum computing
• Information-theoretic bounds on quantum advantage in machine learning
• Anomaly detection in high-energy physics using a quantum autoencoder
• A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance
• Towards provably efficient quantum algorithms for large-scale machine-learning models
• Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning
• One qubit as a Universal Approximant
• Quantum Error Correction of Qudits Beyond Break-even
• Linear-depth quantum circuits for multiqubit controlled gates
• Jet: Fast quantum circuit simulations with parallel task-based tensor-network contraction
• Systematic study of High $E_J/E_C$ transmon qudits up to $d=12$
• Emulating two qubits with a four-level transmon qudit for variational quantum algorithms
• Data re-uploading with a single qudit
• Universal quantum computing with qubits embedded in trapped-ion qudits
• A Multi-Class SWAP-Test Classifier
• QuDiet: A Classical Simulation Platform for Qubit-Qudit Hybrid Quantum Systems
• The Power of One Clean Qubit in Supervised Machine Learning
• Parametrized constant-depth quantum neuron
• Classical Ensembles of Single-Qubit Quantum Variational Circuits for Classification
• QuForge: A Library for Qudits Simulation
• Barren plateaus are amplified by the dimension of qudits