  We develop quantum protocols for anomaly detection and apply them to the task
of credit card fraud detection (FD). First, we establish classical benchmarks
based on supervised and unsupervised machine learning methods, where average
precision is chosen as a robust metric for detecting anomalous data. We focus
on kernel-based approaches for ease of direct comparison, basing our
unsupervised modelling on one-class support vector machines (OC-SVM). Next, we
employ quantum kernels of different type for performing anomaly detection, and
observe that quantum FD can challenge equivalent classical protocols at
increasing number of features (equal to the number of qubits for data
embedding). Performing simulations with registers up to 20 qubits, we find that
quantum kernels with re-uploading demonstrate better average precision, with
the advantage increasing with system size. Specifically, at 20 qubits we reach
the quantum-classical separation of average precision being equal to 15%. We
discuss the prospects of fraud detection with near- and mid-term quantum
hardware, and describe possible future improvements.
