Contemporary quantum computing platforms remain, in essence, programmable physical systems whose control is typically mediated through unitary gate abstractions. While such abstractions provide a uniform interface, they obscure important aspects of the underlying hardware and may limit the exploitation of its full capabilities. Direct operation at the control-pulse level offers a more expressive and physically faithful paradigm, enabling, for instance, the implementation of tailored error-mitigation and optimisation strategies. However, this increased expressivity comes at the cost of greater quantum software development complexity, necessitating structured and accessible tooling.
We present a software framework, integrated within the QML-Essentials package, that extends quantum machine learning (QML) methodologies to encompass pulse-level modelling. By embedding quantum optimal control techniques within a QML setting, our approach enables the seamless combination of gate-based and pulse-level representations. The framework provides a comprehensive suite of modelling and analytical capabilities. In particular, we introduce composable ansatz constructions based on interchangeable building blocks, and support for end-to-end optimisation of pulse parameters. Motivated by the central role of quantum Fourier models, we further incorporate a range of Fourier-analytic diagnostics, complemented by extended measures of entanglement. All performance-critical components are implemented in a high-performance environment using JAX and supported by a dedicated quantum simulator. Taken together, the framework facilitates reproducible and systematic investigations, while bridging the conceptual and practical divide between abstract circuit models and hardware-aware optimisation. It provides a robust foundation for future developments at the intersection of QML and quantum control.
Journal reference
Proceedings of the 2026 IEEE International Conference on Quantum Software (QSW)
Contemporary quantum computing platforms remain, in essence, programmable physical systems whose control is typically mediated through unitary gate abstractions. While such abstractions provide a uniform interface, they obscure important aspects of the underlying hardware and may limit the exploitation of its full capabilities. Direct operation at the control-pulse level offers a more expressive and physically faithful paradigm, enabling, for instance, the implementation of tailored error-mitigation and optimisation strategies. However, this increased expressivity comes at the cost of greater quantum software development complexity, necessitating structured and accessible tooling.
We present a software framework, integrated within the QML-Essentials package, that extends quantum machine learning (QML) methodologies to encompass pulse-level modelling. By embedding quantum optimal control techniques within a QML setting, our approach enables the seamless combination of gate-based and pulse-level representations. The framework provides a comprehensive suite of modelling and analytical capabilities. In particular, we introduce composable ansatz constructions based on interchangeable building blocks, and support for end-to-end optimisation of pulse parameters. Motivated by the central role of quantum Fourier models, we further incorporate a range of Fourier-analytic diagnostics, complemented by extended measures of entanglement. All performance-critical components are implemented in a high-performance environment using JAX and supported by a dedicated quantum simulator. Taken together, the framework facilitates reproducible and systematic investigations, while bridging the conceptual and practical divide between abstract circuit models and hardware-aware optimisation. It provides a robust foundation for future developments at the intersection of QML and quantum control.
In the domain of variational quantum algorithms, quantum Fourier models (QFMs) provide a mathematically well defined structure for quantum machine learning (QML). There has been a substantial amount of work on the scalability and trainability of such models showcasing the potential but also the limitations for the prospective application of QFMs. However, much less is known in the context of pulse-level quantum computing, where the microwave parameters that implement unitary operations on the hardware are used to perform computations directly instead of through the interface of quantum circuits. In this work, we evaluate QFMs through the lens of pulse parameters and link metrics such as expressibility and Fourier coefficient correlation (FCC) to this extended set of variational parameters. We show that while control over pulse shapes does not significantly alter the global expressibility or structural correlations of the Ansatz, it fundamentally alters the local optimisation landscape. For composite gates, independent pulse scalings replace a single logical angle by multiple independently tunable sub-angles. This relaxes the rigid monomial couplings induced by the gate-level parameterisation, and provides gradient descent with higher-dimensional escape routes, decoupling local parameter constraints and significantly boosting performance during training. Following an analytical proof, we show numerical results validating our theory on training a QFM with an exponential (ternary) feature map on a Fourier series with the same frequencies.
Machine Learning (ML) has been widely applied across numerous domains due to its ability to automatically identify informative patterns from data for various tasks. The availability of large-scale data and advanced computational power enables the development of sophisticated models and training strategies, leading to state-of-the-art performance, but it also introduces substantial challenges. Quantum Computing (QC), which exploits quantum mechanisms for computation, has attracted growing attention and significant global investment as it may address these challenges. Consequently, Quantum Machine Learning (QML), the integration of these two fields, has received increasing interest, with a notable rise in related studies in recent years. We are motivated to review these existing contributions regarding quantum circuit-based learning models for classical data analysis and highlight the identified potentials and challenges of this technique. Specifically, we focus not only on QML models, both kernel-based and neural network-based, but also on recent explorations of their integration with classical machine learning layers within hybrid frameworks. Moreover, we examine both theoretical analysis and empirical findings to better understand their capabilities, and we also discuss the efforts on noise-resilient and hardware-efficient QML that could enhance its practicality under current hardware limitations. In addition, we cover several emerging paradigms for advanced quantum circuit design and highlight the adaptability of QML across representative application domains. This study aims to provide an overview of the contributions made to bridge quantum computing and machine learning, offering insights and guidance to support its future development and pave the way for broader adoption in the coming years.
Among notable applications, quantum machine learning (QML) is a promising task that combines quantum computing with machine learning, cited for various types of complex computational problems. This chapter briefly summarizes the frameworks, software platforms, and toolchains currently available for implementing, simulating, and executing hybrid quantum–classical learning algorithms. Major frameworks (e.g., Qiskit Machine Learning, PennyLane, TensorFlow Quantum, and the PyTorch-based toolsets) are analyzed in detail based on their architectural design, functionality, and integration capabilities. They have several key features, such as variational quantum circuits, parameterized quantum gates, automatic differentiation capabilities, and easy integration into a classical deep learning ecosystem. The chapter groups together ongoing research in different architectural paradigms, practical usability aspects, and empirical performance tests. Additionally, it explores aspects of scalability, adaptability to hardware, noise resistance, and reproducibility. The results bring to light elements of the design of trade-offs for creating robust and efficient toolchains for QML, a QML best practice, and guidance for future QML design.
Quantum computing and artificial intelligence (AI) are converging into a distinct research frontier commonly referred to as quantum-enhanced artificial intelligence, or quantum machine learning (QML). This paper presents a conceptual and integrative review of how principles from quantum physics superposition, entanglement, and interference can be embedded into machine learning pipelines to reshape computational paradigms for classification, optimization, and representation learning. Using a structured narrative-review methodology, the study synthesizes theoretical foundations, algorithmic building blocks (quantum feature maps, variational quantum circuits, quantum kernel methods), and application domains spanning drug discovery, finance, materials science, and natural language processing. The review develops a hybrid quantum-classical architecture model and a complexity-comparison framework contrasting classical algorithms with their quantum counterparts, including Grover's search and Shor's factoring algorithm. Findings indicate that while theoretical speedups are well established, practical quantum advantage on noisy intermediate-scale quantum (NISQ) hardware remains constrained by decoherence, barren plateaus, and limited qubit connectivity. The paper contributes a synthesized taxonomy of quantum-enhanced AI methods and an evidence-based research agenda emphasizing error mitigation, hardware-aware ansatz design, and hybrid workload partitioning. The discussion further situates these developments within the broader trajectory of next-generation computing, arguing that near-term value will accrue primarily through hybrid quantum-classical systems rather than fully quantum pipelines. Implications for researchers, industry practitioners, and policymakers are discussed, alongside limitations inherent to a literature-synthesis approach.
Quantum machine learning (QML) has gained significant interest by combining quantum computing and artificial intelligence, two topics that are expected to revolutionize the way of data processing. While gate-based quantum computing uses precisely defined unitary operations on qubits, currently available noisy intermediate-scale quantum (NISQ) devices are not ready for implementations of high-depth circuits. However, machine learning is one of the promising applications to be used on NISQ hardware via parameterized quantum circuits (PQCs). An alternative QML paradigm comes from a different direction: Quantum reservoir computing (QRC) relies on using physical systems as quantum artificial neural networks. Instead of using controlled gate operations, here the system dynamics are controlled by the underlying Hamiltonian, and the machine learning layer is performed at the output weights. Despite their distinct origin, both ML approaches are connected and can formally be mapped onto each other. We discuss this analogy by realizing a transverse-field Ising model on a gate-based quantum computing architecture establishing a fundamental connection on an abstract level between these two very different QML paradigms. This enables us to connect the known expressivity measure of PQC-QML with the quantification of expressiveness of physical dynamical systems.
In this work, we propose a framework in the form of a Python package, specifically designed for the analysis of Quantum Machine Learning models. This framework is based on the PennyLane simulator and facilitates the evaluation and training of Variational Quantum Circuits. It provides additional functionality ranging from the ability to add different types of noise to the classical simulation, over different parameter initialisation strategies, to the calculation of expressibility and entanglement for a given model. As an intrinsic property of Quantum Fourier Models, it provides two methods for calculating the corresponding Fourier spectrum: one via the Fast Fourier Transform and another analytical method based on the expansion of the expectation value using trigonometric polynomials. It also provides a set of predefined approaches that allow a fast and straightforward implementation of Quantum Machine Learning models. With this framework, we extend the PennyLane simulator with a set of tools that allow researchers a more convenient start with Quantum Fourier Models and aim to unify the analysis of Variational Quantum Circuits.