# Single-Qudit Quantum Neural Networks for Multiclass Classification

arXiv: https://arxiv.org/abs/2503.09269 · HTML: https://mlsanity.com/paper/2503.09269/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 59 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Builds on (most cited first, 20 of 20)

- [Large Language Models: A Survey](https://mlsanity.com/paper/2402.06196/) (2024)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Transfer learning in hybrid classical-quantum neural networks](https://mlsanity.com/paper/1912.08278/) (2019)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Efficient-CapsNet: Capsule Network with Self-Attention Routing](https://mlsanity.com/paper/2101.12491/) (2021)
- [Systematic Literature Review: Quantum Machine Learning and its applications](https://mlsanity.com/paper/2201.04093/) (2022)
- [Towards provably efficient quantum algorithms for large-scale machine-learning models](https://mlsanity.com/paper/2303.03428/) (2023)
- [A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance](https://mlsanity.com/paper/2401.11351/) (2024)
- [No Routing Needed Between Capsules](https://mlsanity.com/paper/2001.09136/) (2020)
- [Power and limitations of single-qubit native quantum neural networks](https://mlsanity.com/paper/2205.07848/) (2022)
- [Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning](https://mlsanity.com/paper/2203.15368/) (2022)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [Ensemble learning in CNN augmented with fully connected subnetworks](https://mlsanity.com/paper/2003.08562/) (2020)
- [Multi-Class Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2404.12741/) (2024)
- [Barren plateaus are amplified by the dimension of qudits](https://mlsanity.com/paper/2405.08190/) (2024)
- [Regression and Classification with Single-Qubit Quantum Neural Networks](https://mlsanity.com/paper/2412.09486/) (2024)
- [QuForge: A Library for Qudits Simulation](https://mlsanity.com/paper/2409.17716/) (2024)

## Abstract (arXiv)

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.