  Anomaly detection (AD) involves identifying observations or events that
deviate in some way from the rest of the data. Machine learning techniques have
shown success in automating this process by detecting hidden patterns and
deviations in large-scale data. The potential of quantum computing for machine
learning has been widely recognized, leading to extensive research efforts to
develop suitable quantum machine learning (QML) algorithms. In particular, the
search for QML algorithms for near-term NISQ devices is in full swing. However,
NISQ devices pose additional challenges due to their limited qubit coherence
times, low number of qubits, and high error rates. Kernel methods based on
quantum kernel estimation have emerged as a promising approach to QML on NISQ
devices, offering theoretical guarantees, versatility, and compatibility with
NISQ constraints. Especially support vector machines (SVM) utilizing quantum
kernel estimation have shown success in various supervised learning tasks.
However, in the context of AD, semisupervised learning is of great relevance,
and yet there is limited research published in this area. This paper introduces
an approach to semisupervised AD based on the reconstruction loss of a support
vector regression (SVR) with quantum kernel. This novel model is an alternative
to the variational quantum and quantum kernel one-class classifiers, and is
compared to a quantum autoencoder as quantum baseline and a SVR with
radial-basis-function (RBF) kernel as well as a classical autoencoder as
classical baselines. The models are benchmarked extensively on 10 real-world AD
data sets and one toy data set, and it is shown that our SVR model with quantum
kernel performs better than the SVR with RBF kernel as well as all other
models, achieving highest mean AUC over all data sets. In addition, our QSVR
outperforms the quantum autoencoder on 9 out of 11 data sets.
