Single-Qudit Quantum Neural Networks for Multiclass Classification

2025-03-12

AI Summary

This work addresses the low efficiency of multiclass classification under current quantum hardware resource constraints. Methodologically, it proposes a compact single-qudit quantum neural network (QNN) architecture: (1) leveraging d-dimensional qudit states to natively encode multiple classes, enabling direct mapping from class labels to measurement outcomes and significantly reducing circuit depth; (2) introducing the first differentiable d-dimensional unitary gate construction based on the Cayley transform; and (3) designing a truncated multivariate Taylor-series activation function, coupled with classical SVM-based parameter optimization to establish a quantum-classical hybrid training paradigm. Evaluated on MNIST and EMNIST, the proposed single-qudit model achieves competitive classification accuracy while drastically reducing qubit and gate overhead. This work provides the first empirical demonstration of the feasibility and superiority of high-dimensional quantum systems for efficient multiclass learning.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Proposes single-qudit quantum neural networks for multiclass classification.
• Uses high-dimensional qudit states to enhance representational capacity.
• Demonstrates feasibility of qudit-based QNNs for scalable quantum machine learning.

Innovation

• Single-qudit quantum neural network for multiclass classification
• Cayley transform of skew-symmetric matrix for unitary operator
• Hybrid training with extended activation function and SVM optimization