  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 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 explainability of such
circuits by quantifying the importance of (groups of) gates for specific goals.
To this end, we transfer and adapt the well-established concept of Shapley
values to the quantum realm. 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.
