Supervised time-series classification garners widespread interest because of its applicability throughout a broad application domain including finance, astronomy, biosensors, and many others. In this work, we tackle this problem with hybrid quantum-classical machine learning, deducing pairwise temporal relationships between time-series instances using a time-series Hamiltonian kernel (TSHK). A TSHK is constructed with a sum of inner products generated by quantum states evolved using a parameterized time evolution operator. This sum is then optimally weighted using techniques derived from multiple kernel learning. Because we treat the kernel weighting step as a differentiable convex optimization problem, our method can be regarded as an end-to-end learnable hybrid quantum-classical-convex neural network, or QCC-net, whose output is a data set-generalized kernel function suitable for use in any kernelized machine learning technique such as the support vector machine (SVM). Using our TSHK as input to a SVM, we classify univariate and multivariate time-series using quantum circuit simulators and demonstrate the efficient parallel deployment of the algorithm to 127-qubit superconducting quantum processors using quantum multi-programming.
As quantum computers become increasingly practical, so does the prospect of using quantum computation to improve upon traditional algorithms. Kernel methods in machine learning is one area where such improvements could be realized in the near future. Paired with kernel methods like support-vector machines, small and noisy quantum computers can evaluate classically-hard quantum kernels that capture unique notions of similarity in data. Taking inspiration from techniques in classical machine learning, this work investigates simulated quantum kernels in the context of multiple kernel learning (MKL). We consider pairwise combinations of several classical-classical, quantum-quantum, and quantum-classical kernels in an empirical investigation of their classification performance with support-vector machines. We also introduce a novel approach, which we call QCC-net (quantum-classical-convex neural network), for optimizing the weights of base kernels together with any kernel parameters. We show this approach to be effective for enhancing various performance metrics in an MKL setting. Looking at data with an increasing number of features (up to 13 dimensions), we find parameter training to be important for successfully weighting kernels in some combinations. Using the optimal kernel weights as indicators of relative utility, we find growing contributions from trainable quantum kernels in quantum-classical kernel combinations as the number of features increases. We observe the opposite trend for combinations containing simpler, non-parametric quantum kernels.
Quantum machine learning has emerged as a promising frontier, leveraging the principles of quantum computing to enhance classical algorithms. This paper proposes an optimized Quantum Support Vector Classifier (QSVC) for the classification of the MNIST dataset (a benchmark in handwritten digit recognition). We employ a Chebyshev Parameterized Quantum Circuit (PQC) with an increased number of qubits and layers, and utilize an existing projected quantum kernel method to effectively capture the complex patterns in the data. To enhance model robustness, data augmentation techniques are applied, and dimensionality reduction is performed using Principal Component Analysis (PCA). The proposed QSVC demonstrates competitive accuracy on both the training and testing datasets, highlighting the potential of quantum kernel methods in practical machine learning applications. A comparative analysis with classical Support Vector Machines (SVM) demonstrates the feasibility of quantum methods for high-dimensional classification tasks. Additionally, we investigate the impact of varying the number of qubits in the quantum circuit, providing in-depth insights into the scalability and performance trade-offs of quantum kernel methods.
Abstract We investigated the potential application of quantum computing using the Kronecker kernel to pairwise classification and have devised a way to apply the Harrow-Hassidim-Lloyd (HHL)-based quantum support vector machine algorithm. Pairwise classification can be used to predict relationships among data and is used for problems such as link prediction and chemical interaction prediction. However, in pairwise classification using a Kronecker kernel, it is very costly to calculate the Kronecker product of the kernel matrices when there is a large amount of data. We found that the Kronecker product of kernel matrices can be represented more efficiently in time and space in quantum computing than that in classical computing. We also found that a pairwise classifier can be effectively trained by applying the HHL-based quantum support vector machine algorithm to the Kronecker kernel matrix. In an experiment comparing a classical algorithm with a quantum support vector machine with a Kronecker kernel run on a quantum computing simulator, the misclassification rate of the latter was almost the same as that of the former for the same pairwise classification problem in some cases. This indicates that a quantum support vector machine with a Kronecker kernel algorithm can achieve accuracy equivalent to that of the classical algorithm more efficiently and scalably. This finding paves the way for applying quantum machine learning to predicting relationships in large-scale data.
Radial basis function (RBF) networks are expanded to incorporate quantum kernel functions enabling a new type of hybrid quantum-classical machine learning algorithm. Using this approach, synthetic examples are introduced which allow for proof of concept on interpolation and classification applications. Quantum kernels have primarily been applied to support vector machines (SVMs), however the quantum kernel RBF network offers potential benefit over quantum kernel based SVMs due to the RBF networks ability to perform multi-class classification natively compared to the standard implementation of the SVM.
The field of machine learning has been revolutionized by quantum computing, as it has the capacity to tackle complex problems that are beyond the capabilities of classical computers. One such problem is the efficient classification of speech signals with limited data, employing extracted feature attributes like Mel-scale frequency cepstral coefficients (MFCCs). This study compares the performance of classical machine learning models with a Quantum Support Vector Machine (QKSVM) classifier on a data set with a limited number of audio samples. Interestingly, the quantum kernel method outperformed classical models despite the small sample size. This result can be attributed to the quantum kernel method’s ability to extract high-dimensional features efficiently, allowing it to learn more from fewer samples. The Quantum Kernel Circuit (QKC) is contrived in different variants comprising 13, 8, 7, and 4 qubits. This QKC is built with an Angle Embedding layer, an adjoint version of the Angle Embedding layer, and a Hermitian space observable layer. Our findings demonstrate that the hybrid quantum kernel-based technique outperforms existing classical solutions. Amongst variants, the Quantum support vector machine model with 13 optimal numbers of coefficients is efficient in speech classification with the highest accuracy of 87.32%.
Multi-output time-series forecasting in energy systems is challenging because of nonlinear dynamics, multi-scale seasonality, and strong dependencies across correlated series. In this work, we investigate two hybrid quantum-classical frameworks for multi-stream time-series forecasting on a real Smart Meter dataset comprising 103 household electricity consumption time-series, with experiments executed on the
ibm_marrakesh superconducting quantum processor. The first model, Kernelized Quantum Reservoir Computing with Repeated Measurement (KQRC-RM), combines coupled quantum reservoirs, ancilla-assisted repeated measurement, and kernelized readouts to model temporal dynamics and cross-stream correlations jointly. For a 3-stream time-series input and output, the KQRC-RM model using 114 qubits achieves an MAE of 0.0811 on MPS simulator (36.92\% improvement over its classical analog) whereas performance degrades to an MAE of 0.1524 on hardware. The second, a Projected Quantum Kernel Gaussian Process (QGP), replaces fidelity-based kernels with projected kernels constructed from local reduced-state statistics. Using a topology-aware 100-qubit QGP model to predict 100 multi-output time-series values, we observe 49\% of time-series outputs achieve high-accuracy predictions (MAE
<0.15), with an average MAE of
0.082 for this low-error group. The medium-error regime (MAE
0.15-
0.35) has an average MAE of
0.229, while the high-error regime (MAE
>0.35) has an average MAE of
0.664. Overall, this reduces the average MAE relative to the classical GP baseline by 62.01\% on MPS simulator and 40.37\% on hardware. Together, these results demonstrate the feasibility of hybrid quantum machine learning for multi-input, multi-output time-series forecasting at the 100+ qubit scale on NISQ devices.