  One-class classification is a fundamental problem in pattern recognition with
a wide range of applications. This work presents a semi-supervised quantum
machine learning algorithm for such a problem, which we call a variational
quantum one-class classifier (VQOCC). The algorithm is suitable for noisy
intermediate-scale quantum computing because the VQOCC trains a
fully-parameterized quantum autoencoder with a normal dataset and does not
require decoding. The performance of the VQOCC is compared with that of the
one-class support vector machine (OC-SVM), the kernel principal component
analysis (PCA), and the deep convolutional autoencoder (DCAE) using handwritten
digit and Fashion-MNIST datasets. The numerical experiment examined various
structures of VQOCC by varying data encoding, the number of parameterized
quantum circuit layers, and the size of the latent feature space. The benchmark
shows that the classification performance of VQOCC is comparable to that of
OC-SVM and PCA, although the number of model parameters grows only
logarithmically with the data size. The quantum algorithm outperformed DCAE in
most cases under similar training conditions. Therefore, our algorithm
constitutes an extremely compact and effective machine learning model for
one-class classification.
