QSPE: Enumerating Skeletal Quantum Programs for Quantum Library Testing

TL;DR

QSPE presents a practical framework that extends Skeletal Program Enumeration to quantum libraries, enabling automated, configuration-free generation of large suites of quantum–classical program variants. It substitutes measurement-based validation with statevector-based validation to reduce false positives, and introduces quantum-aware α-equivalence filtering to dramatically cut redundancy. Through seed-based enumeration, optimization-level variants, and cross-library translation (Qiskit→Cirq/Pytket), QSPE generates thousands of variants and reveals 708 miscompilations across Qiskit and Pytket, with 81 cases approved by the developers, evidencing real-world impact. The approach delivers a scalable benchmarking resource and a robust testing workflow for quantum software stacks, with broader implications for cross-library reliability and automated quantum software testing.

Abstract

The rapid advancement of quantum computing has led to the development of various quantum libraries, empowering compilation, simulation, and hardware backend interfaces. However, ensuring the correctness of these libraries remains a fundamental challenge due to the lack of mature testing methodologies. The state-of-the-art tools often rely on domain-specific configurations and expert knowledge, which limits their accessibility and scalability in practice. Furthermore, although these tools demonstrate strong performance, they adopt measurement-based for output validation in testing, which makes them produce false positive reports. To alleviate these limitations, we propose QSPE, a practical approach that follows the differential testing principle and extends the existing approach, SPE, for quantum libraries. QSPE is fully automated, requiring no pre-set configurations or domain expertise, and can effectively generate a large set of diverse program variants that comprehensively explore the quantum compilation space. To mitigate the possible false positive reports, we propose statevector-based validation as an alternative to measurement-based validation. In our experiments, the QSPE approach demonstrates remarkable effectiveness in generating 22,770 program variants across multiple quantum computing platforms. By avoiding $α$-equivalence at the quantum and classical program wise, QSPE can reduce redundant generation and save more than 90\% of execution cost. Finally, the statevector-based validation method assists QSPE to reduce false alarms and effectively detects 708 miscompilations across multiple quantum libraries. Notably, 81 of the discovered bugs have been officially approved and acknowledged by the Qiskit development team, demonstrating the practical impact of our approach.

Figures (10)

• Figure 1: A quantum program example $Q$, its skeleton $\mathbb{Q}$ by applying SPE, and one enumeration result $Q_1$. The quantum code, highlighted in red color, is overlooked by the SPE.
• Figure 2: The overall workflow of our approach.
• Figure 3: Prompt for generating new seed programs by using ChatGPT
• Figure 4: The K and P values with the increasing measurement sampling shots.
• Figure 5: The comparison of the process of getting statevector (in red arrow) and collecting samplings to a distribution (in black arrow).

Theorems & Definitions (1)

• definition 1: Quantum-$\alpha$-Equivalence