  Quantum computing offers significant speedup compared to classical computing,
which has led to a growing interest among users in learning and applying
quantum computing across various applications. However, quantum circuits, which
are fundamental for implementing quantum algorithms, can be challenging for
users to understand due to their underlying logic, such as the temporal
evolution of quantum states and the effect of quantum amplitudes on the
probability of basis quantum states. To fill this research gap, we propose
QuantumEyes, an interactive visual analytics system to enhance the
interpretability of quantum circuits through both global and local levels. For
the global-level analysis, we present three coupled visualizations to delineate
the changes of quantum states and the underlying reasons: a Probability Summary
View to overview the probability evolution of quantum states; a State Evolution
View to enable an in-depth analysis of the influence of quantum gates on the
quantum states; a Gate Explanation View to show the individual qubit states and
facilitate a better understanding of the effect of quantum gates. For the
local-level analysis, we design a novel geometrical visualization Dandelion
Chart to explicitly reveal how the quantum amplitudes affect the probability of
the quantum state. We thoroughly evaluated QuantumEyes as well as the novel
QuantumEyes integrated into it through two case studies on different types of
quantum algorithms and in-depth expert interviews with 12 domain experts. The
results demonstrate the effectiveness and usability of our approach in
enhancing the interpretability of quantum circuits.
