Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large datasets. In recent work, quantum randomized measurements kernels and variable subsampling were proposed, as two independent methods to address this problem. The former achieves higher average precision, but suffers from variance, while the latter achieves linear complexity to data size and has lower variance. The current work focuses instead on combining these two methods, along with rotated feature bagging, to achieve linear time complexity both to data size and to number of features. Despite their instability, the resulting models exhibit considerably higher performance and faster training and testing times.
Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large datasets. In recent work, quantum randomized measurements kernels and variable subsampling were proposed, as two independent methods to address this problem. The former achieves higher average precision, but suffers from variance, while the latter achieves linear complexity to data size and has lower variance. The current work focuses instead on combining these two methods, along with rotated feature bagging, to achieve linear time complexity both to data size and to number of features. Despite their instability, the resulting models exhibit considerably higher performance and faster training and testing times.
Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for its classically challenging representational capacity, notable improvements in average precision compared to classical counterparts were observed in previous studies. Conventional calculations of these kernels, however, present a quadratic time complexity concerning data size, posing challenges in practical applications. To mitigate this, we explore two distinct approaches: utilizing randomized measurements to evaluate the quantum kernel and implementing the variable subsampling ensemble method, both targeting linear time complexity. Experimental results demonstrate a substantial reduction in training and inference times by up to 95\% and 25\% respectively, employing these methods. Although unstable, the average precision of randomized measurements discernibly surpasses that of the classical Radial Basis Function kernel, suggesting a promising direction for further research in scalable, efficient quantum computing applications in machine learning.
Anomaly detection, an important task in data analysis, 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 anomaly detection, semisupervised learning is of great relevance, and yet there is limited research published in this area. This paper introduces an approach to semisupervised anomaly detection 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 anomaly detection 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.
Whether in fundamental physics, cybersecurity or finance, the detection of anomalies with machine learning techniques is a highly relevant and active field of research, as it potentially accelerates the discovery of novel physics or criminal activities. We provide a systematic analysis of the generalization properties of the One-Class Support Vector Machine (OCSVM) algorithm, using projected quantum kernels for a realistic dataset of the latter application. These results were both theoretically simulated and experimentally validated on trapped-ion and superconducting quantum processors, by leveraging partial state tomography to obtain precise approximations of the quantum states that are used to estimate the quantum kernels. Moreover, we analyzed both platforms respective hardware-efficient feature maps over a wide range of anomaly ratios and showed that for our financial dataset in all anomaly regimes, the quantum-enhanced OCSVMs lead to better generalization properties compared to the purely classical approach. As such our work bridges the gap between theory and practice in the noisy intermediate scale quantum (NISQ) era and paves the path towards useful quantum applications.
Abstract Whether in fundamental physics, cybersecurity or finance, the detection of anomalies with machine learning techniques is a highly relevant and active field of research, as it potentially accelerates the discovery of novel physics or criminal activities. We provide a systematic analysis of the generalization properties of the One-Class Support Vector Machine (OCSVM) algorithm, using projected quantum kernels for a realistic dataset of the latter application. These results were both theoretically simulated and experimentally validated on trapped-ion and superconducting quantum processors, by leveraging partial state tomography to obtain precise approximations of the quantum states that are used to estimate the quantum kernels. Moreover, we analyzed both platforms respective hardware-efficient feature maps over a wide range of anomaly ratios and showed that for our financial dataset in all anomaly regimes, the quantum-enhanced OCSVMs lead to better generalization properties compared to the purely classical approach. As such our work bridges the gap between theory and practice in the noisy intermediate scale quantum (NISQ) era and paves the path towards useful quantum applications.
Quantum kernel methods are promising for near-term quantum machine learning, but their training costs are driven by the quadratic scaling of Gram-matrix construction and the measurement cost of estimating individual kernel values. In this work, we investigate one-class anomaly detection as a resource-efficient operating regime for training non-variational quantum kernel models. Using the ULB Credit Card Fraud Detection dataset, we evaluate three quantum feature maps across training-set sizes and qubit counts. Power-law saturation models reveal strong diminishing returns with increasing training data, with 500-sample models retaining approximately 90--93\% of their fitted asymptotic average precision (AP). We further observe no severe exponential concentration among the evaluated feature maps over the investigated qubit range, thereby avoiding the exponentially increasing measurement requirements associated with that regime. Finally, Nyström approximation reduces kernel construction from O(N2) to O(Nm) evaluations, with QSVR retaining 94--97\% of its exact-kernel AP using only five landmarks. For ZZ-QSVR, downsampling from 4,000 to 500 training samples and applying a five-landmark approximation decreases the number of required kernel evaluations from approximately 8.0 million to 2,485, a reduction of more than 3,200-fold, while AP decreases from 0.812 to 0.737. Under the minimum IonQ pricing assumption considered here, this corresponds to an illustrative reduction in quantum kernel training cost from approximately $1.34 billion to $417{,}480. These results demonstrate that training-set reduction and low-rank approximation can substantially reduce the resources required to train non-variational quantum kernel anomaly detectors while retaining meaningful anomaly-discrimination performance.
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.