Quantum support vector data description for anomaly detection

TL;DR

This paper introduces QSVDD, a quantum algorithm for anomaly detection that uses a shallow quantum circuit to efficiently learn a hypersphere enclosing normal data, outperforming some existing methods.

Contribution

The paper presents a novel quantum support vector data description (QSVDD) algorithm optimized for NISQ devices, with a compact model and superior performance in anomaly detection tasks.

Findings

QSVDD outperforms quantum autoencoder and deep learning methods on MNIST datasets.

QSVDD has a logarithmic growth in parameters with input size, enabling efficient training.

QSVDD demonstrates strong anomaly detection performance with a simple quantum model.

Abstract

Anomaly detection is a critical problem in data analysis and pattern recognition, finding applications in various domains. We introduce quantum support vector data description (QSVDD), an unsupervised learning algorithm designed for anomaly detection. QSVDD utilizes a shallow-depth quantum circuit to learn a minimum-volume hypersphere that tightly encloses normal data, tailored for the constraints of noisy intermediate-scale quantum (NISQ) computing. Simulation results on the MNIST and Fashion MNIST image datasets demonstrate that QSVDD outperforms both quantum autoencoder and deep learning-based approaches under similar training conditions. Notably, QSVDD offers the advantage of training an extremely small number of model parameters, which grows logarithmically with the number of input qubits. This enables efficient learning with a simple training landscape, presenting a compact quantum machine learning model with strong performance for anomaly detection.