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.

翻译：异常检测（AD）涉及识别在某种程度上偏离其余数据的观测或事件。机器学习技术通过在大规模数据中检测隐藏模式和偏离，在自动化这一过程中展现出成功。量子计算在机器学习领域的潜力已得到广泛认可，由此催生了大量旨在开发合适量子机器学习（QML）算法的研究。尤其是针对近期NISQ设备的QML算法研究正如火如荼地进行。然而，NISQ设备因其有限的量子比特相干时间、低量子比特数和高错误率而带来额外挑战。基于量子核估计的核方法已成为NISQ设备上QML的一种有前景的途径，提供了理论保证、多功能性以及与NISQ约束的兼容性。特别是利用量子核估计的支持向量机（SVM）已在各种监督学习任务中取得成功。然而，在异常检测背景下，半监督学习具有重要相关性，但该领域已发表的研究有限。本文提出了一种基于具有量子核的支持向量回归（SVR）重建损失的半监督异常检测方法。这一新颖模型是变分量子与量子核单类分类器的替代方案，并与作为量子基线的量子自编码器、具有径向基函数（RBF）核的SVR以及作为经典基线的经典自编码器进行了比较。这些模型在10个真实世界异常检测数据集和1个人工数据集上进行了广泛基准测试，结果显示，我们的量子核SVR模型在性能上优于具有RBF核的SVR以及其他所有模型，在所有数据集上达到了最高的平均AUC。此外，我们的QSVR在11个数据集中的9个上优于量子自编码器。