Assessing Superposition-Targeted Coverage Criteria for Quantum Neural Networks

TL;DR

The paper addresses reliability and robustness in Quantum Neural Networks (QNNs) by proposing three superposition-targeted coverage criteria—$K$-cell State Coverage ($KSC$), State Corner Coverage ($SCC$), and Top-$k$ State Coverage ($TSC$)—to quantify state-space exploration in test suites. It presents a profiling workflow that derives major and corner regions from training data via basis-state probabilities and evaluates the criteria on MNIST and FashionMNIST using four QNN architectures, under varying circuit scales, shot budgets, and noise conditions. Results show SCC and TSC are particularly sensitive to input diversity and robust to moderate quantum noise and finite shots, with KSC offering complementary insights; ablations reveal how hyperparameters and data distributions shape absolute values while preserving qualitative trends. The work provides practical guidance for QNN testing and highlights challenges for scaling up, including the need for refined granularity and evaluation protocols in realistic quantum execution environments.

Abstract

Quantum Neural Networks (QNNs) have achieved initial success in various tasks by integrating quantum computing and neural networks. However, growing concerns about their reliability and robustness highlight the need for systematic testing. Unfortunately, current testing methods for QNNs remain underdeveloped, with limited practical utility and insufficient empirical evaluation. As an initial effort, we design a set of superposition-targeted coverage criteria to evaluate QNN state exploration embedded in test suites. To characterize the effectiveness, scalability, and robustness of the criteria, we conduct a comprehensive empirical study using benchmark datasets and QNN architectures. We first evaluate their sensitivity to input diversity under multiple data settings, and analyze their correlation with the number of injected faults. We then assess their scalability to increasing circuit scales. The robustness is further studied under practical quantum constraints including insufficient measurement and quantum noise. The results demonstrate the effectiveness of quantifying test adequacy and the potential applicability to larger-scale circuits and realistic quantum execution, while also revealing some limitations. Finally, we provide insights and recommendations for future QNN testing.

Figures (7)

• Figure 1: Example of a parameterized quantum circuit (PQC).
• Figure 2: A general structure of QNN.
• Figure 3: The overview of assessing coverage criteria for QNNs. During testing execution, it involves profiling model behaviors and computing coverage. Subsequently, empirical evaluation is conducted based on coverage results to analyze their effectiveness, scalability and robustness.
• Figure 4: Coverage results obtained by test suites containing different proportions of faults (MNIST).
• Figure 5: Coverage results obtained by test suites containing different proportions of faults (FashionMNIST).