Neural quantum support vector data description for one-class classification

TL;DR

NQSVDD is introduced, a classical-quantum hybrid framework for OCC that performs end-to-end optimized hierarchical representation learning that achieves competitive or superior AUC performance compared to classical Deep SVDD and quantum baselines while maintaining parameter efficiency and robustness under realistic noise conditions.

Abstract

One-class classification (OCC) is a fundamental problem in machine learning with numerous applications, such as anomaly detection and quality control. With the increasing complexity and dimensionality of modern datasets, there is a growing demand for advanced OCC techniques with better expressivity and efficiency. We introduce Neural Quantum Support Vector Data Description (NQSVDD), a classical-quantum hybrid framework for OCC that performs end-to-end optimized hierarchical representation learning. NQSVDD integrates a classical neural network with trainable quantum data encoding and a variational quantum circuit, enabling the model to learn nonlinear feature transformations tailored to the OCC objective. The hybrid architecture maps input data into an intermediate high-dimensional feature space and subsequently projects it into a compact latent space defined through quantum measurements. Importantly, both the feature embedding and the latent representation are jointly optimized such that normal data form a compact cluster, for which a minimum-volume enclosing hypersphere provides an effective decision boundary. Experimental evaluations on benchmark datasets demonstrate that NQSVDD achieves competitive or superior AUC performance compared to classical Deep SVDD and quantum baselines, while maintaining parameter efficiency and robustness under realistic noise conditions.

Figures (7)

• Figure 1: Overview of NQSVDD. Classical neural network layers extract features from complex input data. The output of classical layers is encoded into quantum state using ZZ feature embedding. Alternating repetition of the embedding layers and parameterized quantum layers makes the expressive power of the embedding richer. After the state preparation, variational quantum circuit and a set of Pauli measurements map the features into the latent space. The combination of classical layers, denoted as $\phi_{c}(\cdot;\boldsymbol{\mathcal{W}})$, and quantum layers, denoted as $\phi_{q}(\cdot;\boldsymbol{\theta})$, construct the overall feature mapping for OCC, trained to find the optimal latent space and hypersphere.
• Figure 2: The parameterized two-qubit gate that can generate an arbitrary two-qubit unitary transformation in $SU(4)$, requiring $15$ real parameters. $R_{i}(\theta)$ is a rotation gate of $i$ axis of Bloch sphere, and $U_{3}(\theta, \phi, \lambda)=R_{z}(\phi)R_{x}(-\pi/2)R_{z}(\theta)R_{x}(\pi/2)R_{z}(\lambda)$. This two-qubit ansatz is applied for parameterized unitary layers in data embedding, and convolutional layers in QCNN.
• Figure 3: Avg. AUC (%) and std. (error bar) on (a) MNIST and (b) Fashion-MNIST datasets. NQSVDD, QSVDD and DSVDD have $1105$, $75$ and $2152$ number of parameters, respectively. Each bar represents the average score of $10$ repetitions.
• Figure A.1: Avg. AUC (%) and std. (error bar) by the dimension of latent space on (a) "0" of MNIST and (b) "T-shirt" of Fashion-MNIST datasets with $10$ random seeds per latent dimension.
• Figure A.2: Avg. AUC (%) and std. (error bar) for different numbers of embedding layers in NQSVDD. For MNIST and Fashion MNIST, the average and std. of AUC scores are computed over all target-class experiments, using 10 random seeds per target class (100 experiments per the number of embedding layers). For Credit Card Transaction and Network Intrusion datasets, results are averaged over 10 random seeds for each number of embedding layers.