  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.
