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。机器学习技术通过检测大规模数据中的隐藏模式和偏差，在自动化该过程方面取得了成功。量子计算在机器学习中的潜力已得到广泛认可，促使大量研究工作致力于开发合适的量子机器学习（QML）算法。特别是面向近期NISQ设备的QML算法搜索正在全面展开。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的有前景途径，具有理论保证、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）在多种监督学习任务中取得了成功。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量子核支持向量回归（SVR）重建损失的半监督AD方法。该新颖模型是变分量子分类器和量子核单类分类器的替代方案，并与量子自编码器（作为量子基线）、径向基函数（RBF）核SVR以及经典自编码器（作为经典基线）进行了比较。这些模型在10个真实AD数据集和1个模拟数据集上进行了广泛基准测试，结果表明，我们的量子核SVR模型性能优于RBF核SVR及其他所有模型，在所有数据集上实现了最高平均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。