Abstract Variational quantum machine learning (VQML) models based on parameterized quantum circuits (PQC) have been expected to offer a potential quantum advantage for machine learning (ML) applications. However, comparison between VQML models and their classical counterparts is hard due to the lack of interpretability of VQML models. In this study, we introduce a graphical approach to analyze the PQC and the corresponding operation of VQML models to deal with this problem. In particular, we utilize the Stokes representation of quantum states to treat VQML models as network models based on the corresponding representations of basic gates. From this approach, we suggest the notion of active paths in the networks and relate the expressivity of VQML models with it. We investigate the growth of active paths in VQML models and observe that the expressivity of VQML models can be significantly limited for certain cases. Then we construct classical models inspired by our graphical interpretation of VQML models and show that they can emulate or outperform the outputs of VQML models for these cases. Our result provides a new way to interpret the operation of VQML models and facilitates the interconnection between quantum and classical ML areas.
Abstract Variational quantum machine learning (VQML) models based on parameterized quantum circuits (PQC) have been expected to offer a potential quantum advantage for machine learning (ML) applications. However, comparison between VQML models and their classical counterparts is hard due to the lack of interpretability of VQML models. In this study, we introduce a graphical approach to analyze the PQC and the corresponding operation of VQML models to deal with this problem. In particular, we utilize the Stokes representation of quantum states to treat VQML models as network models based on the corresponding representations of basic gates. From this approach, we suggest the notion of active paths in the networks and relate the expressivity of VQML models with it. We investigate the growth of active paths in VQML models and observe that the expressivity of VQML models can be significantly limited for certain cases. Then we construct classical models inspired by our graphical interpretation of VQML models and show that they can emulate or outperform the outputs of VQML models for these cases. Our result provides a new way to interpret the operation of VQML models and facilitates the interconnection between quantum and classical ML areas.
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.
Abstract Methods of artificial intelligence (AI) and especially machine learning (ML) have been growing ever more complex, and at the same time have more and more impact on people’s lives. This leads to explainable AI (XAI) manifesting itself as an important research field that helps humans to better comprehend ML systems. In parallel, quantum machine learning (QML) is emerging with the ongoing improvement of quantum computing hardware combined with its increasing availability via cloud services. QML enables quantum-enhanced ML in which quantum mechanics is exploited to facilitate ML tasks, typically in the form of quantum-classical hybrid algorithms that combine quantum and classical resources. Quantum gates constitute the building blocks of gate-based quantum hardware and form circuits that can be used for quantum computations. For QML applications, quantum circuits are typically parameterized and their parameters are optimized classically such that a suitably defined objective function is minimized. Inspired by XAI, we raise the question of the explainability of such circuits by quantifying the importance of (groups of) gates for specific goals. To this end, we apply the well-established concept of Shapley values. The resulting attributions can be interpreted as explanations for why a specific circuit works well for a given task, improving the understanding of how to construct parameterized (or variational) quantum circuits, and fostering their human interpretability in general. An experimental evaluation on simulators and two superconducting quantum hardware devices demonstrates the benefits of the proposed framework for classification, generative modeling, transpilation, and optimization. Furthermore, our results shed some light on the role of specific gates in popular QML approaches.
The quest for successful variational quantum machine learning (QML) relies on the design of suitable parametrized quantum circuits (PQCs), as analogues to neural networks in classical machine learning. Successful QML models must fulfill the properties of trainability and non-dequantization, among others. Recent works have highlighted an intricate interplay between trainability and dequantization of such models, which is still unresolved. In this work we contribute to this debate from the perspective of machine learning, proving a number of results identifying, among others when trainability and non-dequantization are not mutually exclusive. We begin by providing a number of new somewhat broader definitions of the relevant concepts, compared to what is found in other literature, which are operationally motivated, and consistent with prior art. With these precise definitions given and motivated, we then study the relation between trainability and dequantization of variational QML. Next, we also discuss the degrees of "variationalness" of QML models, where we distinguish between models like the hardware efficient ansatz and quantum kernel methods. Finally, we introduce recipes for building PQC-based QML models which are both trainable and nondequantizable, and corresponding to different degrees of variationalness. We do not address the practical utility for such models. Our work however does point toward a way forward for finding more general constructions, for which finding applications may become feasible.
Expressibility is a crucial factor of a Parameterized Quantum Circuit (PQC). In the context of Variational Quantum Algorithms (VQA) based Quantum Machine Learning (QML), a QML model composed of highly expressible PQC and sufficient number of qubits is theoretically capable of approximating any arbitrary continuous function. While much research has explored the relationship between expressibility and learning performance, as well as the number of layers in PQCs, the connection between expressibility and PQC structure has received comparatively less attention. In this paper, we analyze the connection between expressibility and the types of quantum gates within PQCs using a Gradient Boosting Tree model and SHapley Additive exPlanations (SHAP) values. Our analysis is performed on 1,615 instances of PQC derived from 19 PQC topologies, each with 2-18 qubits and 1-5 layers. The findings of our analysis provide guidance for designing highly expressible PQCs, suggesting the integration of more RX or RY gates while maintaining a careful balance with the number of CNOT gates. Furthermore, our evaluation offers an additional evidence of expressibility saturation, as observed by previous studies.
Abstract Quantum Machine Learning (QML) offers tremendous potential but is currently limited by the availability of qubits. We introduce an innovative approach that utilizes pre-trained neural networks to enhance Variational Quantum Circuits (VQC). This technique effectively separates approximation error from qubit count and removes the need for restrictive conditions, making QML more viable for real-world applications. Our method significantly improves parameter optimization for VQC while delivering notable gains in representation and generalization capabilities, as evidenced by rigorous theoretical analysis and extensive empirical testing on quantum dot classification tasks. Moreover, our results extend to applications such as human genome analysis, demonstrating the broad applicability of our approach. By addressing the constraints of current quantum hardware, our work paves the way for a new era of advanced QML applications, unlocking the full potential of quantum computing in fields such as machine learning, materials science, medicine, mimetics, and various interdisciplinary areas.
Abstract Hybrid quantum–classical systems make it possible to utilize existing quantum computers to their fullest extent. Within this framework, parameterized quantum circuits can be regarded as machine learning models with remarkable expressive power. This Review presents the components of these models and discusses their application to a variety of data-driven tasks, such as supervised learning and generative modeling. With an increasing number of experimental demonstrations carried out on actual quantum hardware and with software being actively developed, this rapidly growing field is poised to have a broad spectrum of real-world applications.