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Quantum Information Processing

Quantum kernel estimation-based quantum support vector regression

Xiaojian Zhou, Jieyao Yu, Junfan Tan, Ting Jiang

Published Jan 23, 2024• 27 citations
Publisher
DOI
10.1007/s11128-023-04231-7

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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.

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Quantum Support Vector Regression (QSVR) has become an exciting prospect of modeling the nonlinear relationship of high-dimensional data by using a kernel method. Nevertheless, the overall assessment of the whole QSVR pipeline, including preprocessing and dimensionality reduction, quantum embedding, shot-based kernel estimation, and noise-aware analysis, is not widespread. This paper introduces a working Python implementation of the QSVR framework that combines a principal component analysis (PCA)-to-qubit embedding, a 1024-shot quantum kernel implementation, and 1024-shot 1/2-SVR optimization on financial time-series and credit transaction regression problems. Classical features are normalized and minimized to around 20 major features that capture 95% of the variance in the data before being angle-based RY embedded using a depth-3 entangling circuit. Quantum kernels are built through state-overlap estimation on finite-shot constraints, and they are trained by cross-validated optimization. The robustness of the proposed framework is measured in both noise-free and simulator-generated noise conditions in case of controlled noise approximations. Experimentation indicates improved regression performance than that of an RBF-SVR baseline with the same preprocessing and validation conditions. The suggested workflow designates the concept of reproducibility, benchmarking control, and feasible noise-conscious evaluation, which offers a systematic reference structure to subsequent research within near-term quantum machine learning.

IEEE Access•Jan 1, 2026•1 citation
This work presents an over-the-air (OTA) OFDM software-defined radio (SDR) prototype using GNU Radio and two HackRF One devices to evaluate classical and quantumkernel channel estimation.LS, LMMSE, Support Vector Regression (SVR), and quantum-kernel SVR (QSVR) are compared on identical received IQ samples under controlled Gaussian and impulsive noise.BER, packet recovery, latency, and processing throughput are evaluated.Results show that the kernel-based estimators remain competitive with conventional approaches, demonstrating the feasibility of quantum-kernel channel estimation in a complete over-the-air SDR receiver.
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.
Quantum Support Vector Regression (QSVR) has become an exciting prospect of modeling the nonlinear relationship of high-dimensional data by using a kernel method. Nevertheless, the overall assessment of the whole QSVR pipeline, including preprocessing and dimensionality reduction, quantum embedding, shot-based kernel estimation, and noise-aware analysis, is not widespread. This paper introduces a working Python implementation of the QSVR framework that combines a principal component analysis (PCA)-to-qubit embedding, a 1024-shot quantum kernel implementation, and 1024-shot 1/2-SVR optimization on financial time-series and credit transaction regression problems. Classical features are normalized and minimized to around 20 major features that capture 95% of the variance in the data before being angle-based RY embedded using a depth-3 entangling circuit. Quantum kernels are built through state-overlap estimation on finite-shot constraints, and they are trained by cross-validated optimization. The robustness of the proposed framework is measured in both noise-free and simulator-generated noise conditions in case of controlled noise approximations. Experimentation indicates improved regression performance than that of an RBF-SVR baseline with the same preprocessing and validation conditions. The suggested workflow designates the concept of reproducibility, benchmarking control, and feasible noise-conscious evaluation, which offers a systematic reference structure to subsequent research within near-term quantum machine learning.