The widespread benefits of classical machine learning along with promised speedups by quantum algorithms over their best performing classical counterparts have motivated development of quantum machine learning algorithms that combine these two approaches. Quantum Kernel Methods (QKMs) [22, 49] describe one such combination, which seeks to leverage the high dimensional Hilbert space over quantum states to perform classification on encoded classical data. In this work I present an analysis of QKM algorithms used to encode and classify real data using a quantum processor, aided by a suite of custom noise models and hardware optimizations. I introduce and validate techniques for error mitigation and readout error correction designed specifically for this algorithm/hardware combination. Though I do not achieve high accuracy with one type of QKM-based classifier, I provide evidence for possible fundamental limitations to the QKM as well as hardware limitations that are unaccounted for by a reasonable Markovian noise model.
The widespread benefits of classical machine learning along with promised speedups by quantum algorithms over their best performing classical counterparts have motivated development of quantum machine learning algorithms that combine these two approaches. Quantum Kernel Methods (QKMs) [22, 49] describe one such combination, which seeks to leverage the high dimensional Hilbert space over quantum states to perform classification on encoded classical data. In this work I present an analysis of QKM algorithms used to encode and classify real data using a quantum processor, aided by a suite of custom noise models and hardware optimizations. I introduce and validate techniques for error mitigation and readout error correction designed specifically for this algorithm/hardware combination. Though I do not achieve high accuracy with one type of QKM-based classifier, I provide evidence for possible fundamental limitations to the QKM as well as hardware limitations that are unaccounted for by a reasonable Markovian noise model.
Machine Learning has been remarkably successful and is transforming the way real life problems are solved. Quantum Computing is a developing field that utilizes different quantum phenomena for computational speedup. Quantum Machine Learning (QML) focuses on combining these two fields in a meaningful manner. Quantum kernels are among the state of the art approaches to QML. This thesis reproduces the existing work on quantum kernels and then expands on its real life application. These applications are addressed through two types of studies, comparison of quantum kernel based models with classical ML models and analysis of their performance on the present day error prone quantum hardware using noise simulation. Both of these studies are implemented using Qiskit in Python. The comparison results show that the quantum kernels can achieve better results than their classical counterpart. Noise simulations show that the model is resilient to lower levels of noise. However, further investigation is needed to explain the overall noise trends.
Quantum kernel methods (QKMs) have emerged as a prominent framework for supervised quantum machine learning. Unlike variational quantum algorithms, which rely on gradient-based optimisation and may suffer from issues such as barren plateaus, non-variational QKMs employ fixed quantum feature maps, with model selection performed classically via convex optimisation and cross-validation. This separation of quantum feature embedding from classical training ensures stable optimisation while leveraging quantum circuits to encode data in high-dimensional Hilbert spaces. In this review, we provide a thorough analysis of non-variational supervised QKMs, covering their foundations in classical kernel theory, constructions of fidelity and projected quantum kernels, and methods for their estimation in practice. We examine frameworks for assessing quantum advantage, including generalisation bounds and necessary conditions for separation from classical models, and analyse key challenges such as exponential concentration, dequantisation via tensor-network methods, and the spectral properties of kernel integral operators. We further discuss structured problem classes that may enable advantage, and synthesise insights from comparative and hardware studies. Overall, this review aims to clarify the regimes in which QKMs may offer genuine advantages, and to delineate the conceptual, methodological, and technical obstacles that must be overcome for practical quantum-enhanced learning.
The discovery of quantum algorithms offering provable advantages over the best known classical alternatives, together with the parallel ongoing revolution brought about by classical artificial intelligence, motivates a search for applications of quantum information processing methods to machine learning. Among several proposals in this domain, quantum kernel methods have emerged as particularly promising candidates. However, while some rigorous speedups on certain highly specific problems have been formally proven, only empirical proof-of-principle results have been reported so far for real-world datasets. Moreover, no systematic procedure is known, in general, to fine tune and optimize the performances of kernel-based quantum classification algorithms. At the same time, certain limitations such as kernel concentration effects-hindering the trainability of quantum classifiers-have also been recently pointed out. In this work, we propose several general-purpose optimization methods and best practices designed to enhance the practical usefulness of fidelity-based quantum classification algorithms. Specifically, we first describe a data pre-processing strategy that, by preserving the relevant relationships between data points when processed through quantum feature maps, substantially alleviates the effect of kernel concentration on structured datasets. We also introduce a classical post-processing method that, based on standard fidelity measures estimated on a quantum processor, yields non-linear decision boundaries in the feature Hilbert space, thus achieving the quantum counterpart of the radial basis functions technique that is widely employed in classical kernel methods. Finally, we apply the so-called quantum metric learning protocol to engineer and adjust trainable quantum embeddings, demonstrating substantial performance improvements on several paradigmatic real-world classification tasks.
Quantum machine learning could possibly become a valuable alternative to classical machine learning for applications in high energy physics by offering computational speedups. In this study, we employ a support vector machine with a quantum kernel estimator (QSVM-Kernel method) to a recent LHC flagship physics analysis: ttH (Higgs boson production in association with a top quark pair). In our quantum simulation study using up to 20 qubits and up to 50000 events, the QSVM-Kernel method performs as well as its classical counterparts in three different platforms from Google Tensorflow Quantum, IBM Quantum, and Amazon Braket. Additionally, using 15 qubits and 100 events, the application of the QSVM-Kernel method on the IBM superconducting quantum hardware approaches the performance of a noiseless quantum simulator. Our study confirms that the QSVM-Kernel method can use the large dimensionality of the quantum Hilbert space to replace the classical feature space in realistic physics data sets.
Abstract Since the entry of kernel theory in the field of quantum machine learning, quantum kernel methods (QKMs) have gained increasing attention with regard to both probing promising applications and delivering intriguing research insights. Benchmarking these methods is crucial to gain robust insights and to understand their practical utility. In this work, we present a comprehensive large-scale study examining QKMs based on fidelity quantum kernels (FQKs) and projected quantum kernels (PQKs) across a manifold of design choices. Our investigation encompasses both classification and regression tasks for five dataset families and 64 datasets, systematically comparing the use of FQKs and PQKs quantum support vector machines and kernel ridge regression. This resulted in over 20,000 models that were trained and optimized using a state-of-the-art hyperparameter search to ensure robust and comprehensive insights. We delve into the importance of hyperparameters on model performance scores and support our findings through rigorous correlation analyses. Additionally, we provide an in-depth analysis addressing the design freedom of PQKs and explore the underlying principles responsible for learning. Our goal is not to identify the best-performing model for a specific task but to uncover the mechanisms that lead to effective QKMs and reveal universal patterns.
Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs), constructed by embedding data into the Hilbert space of a quantum computer, are a particular quantum kernel technique that is particularly suitable for noisy intermediate-scale quantum devices. Unfortunately, kernel methods face three major problems: Constructing the kernel matrix has quadratic computational complexity in the number of training samples, choosing the right kernel function is nontrivial, and the effects of noise are unknown. In this work, we addressed the latter two. In particular, we introduced the notion of trainable QEKs, based on the idea of classical model optimization methods. To train the parameters of the QEK, we proposed the use of kernel-target alignment. We verified the feasibility of this method, and showed that for our experimental setup we could reduce the training error significantly. Furthermore, we investigated the effects of device and finite sampling noise, and we evaluated various mitigation techniques numerically on classical hardware. We took the best performing strategy and evaluated it on data from a real quantum processing unit. We found that using this mitigation strategy demonstrated an increased kernel matrix quality.