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Lecture notes in computer science

QEMI: A Quantum Software Stacks Testing Framework via Equivalence Modulo Inputs

Junjie Luo, Shangzhou Xia, Fuyuan Zhang, Jianjun Zhao

Published Jan 1, 2026• 0 citations
Publisher
DOI
10.1007/978-3-032-22774-4_8

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QEMI: A Quantum Software Stacks Testing Framework via Equivalence Modulo Inputs

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As quantum algorithms and hardware continue to evolve, ensuring the correctness of the quantum software stack (QSS) has become increasingly important. However, testing QSSes remains challenging due to the oracle problem, i.e., the lack of a reliable ground truth for expected program behavior. Existing metamorphic testing approaches often rely on equivalent circuit transformations, backend modifications, or parameter tuning to address this issue. In this work, inspired by Equivalence Modulo Inputs (EMI), we propose Quantum EMI (QEMI), a new testing approach for QSSes. Our key contributions include: (1) a random quantum program generator that produces code with dead code based on quantum control-flow structures, and (2) an adaptation of the EMI technique from classical compiler testing to generate variants by removing dead code. By comparing the behavior of these variants, we can detect potential bugs in QSS implementations. We applied QEMI to Qiskit, Q#, and Cirq, and successfully identified 11 crash bugs and 1 behavioral inconsistency. QEMI expands the limited set of testing techniques available for quantum software stacks by going beyond structural transformations and incorporating semantics-preserving ones into quantum program analysis.

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As quantum computing transitions from theoretical concepts to commercially available quantum processing units, ensuring the quality, reliability, and correctness of quantum software systems has become paramount. The unique challenges of quantum software testing have necessitated the adaptation of classical software engineering techniques to the quantum domain. One such technique is fuzz testing, or fuzzing, an automated software testing technique that generates large volumes of inputs to identify bugs and unexpected behaviors. In this work we provide a comprehensive examination of how fuzz testing has been successfully applied to quantum computing. We analyze the application of fuzzing across the quantum ecosystem, from testing quantum programs to verifying quantum software stacks, quantum compilers, and quantum simulators. This survey establishes the foundation for understanding how fuzz testing can ensure the reliability and correctness of quantum software systems and outlines promising future research directions.

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As quantum algorithms and hardware continue to evolve, ensuring the correctness of the quantum software stack (QSS) has become increasingly important. However, testing QSSes remains challenging due to the oracle problem, i.e., the lack of a reliable ground truth for expected program behavior. Existing metamorphic testing approaches often rely on equivalent circuit transformations, backend modifications, or parameter tuning to address this issue. In this work, inspired by Equivalence Modulo Inputs (EMI), we propose Quantum EMI (QEMI), a new testing approach for QSSes. Our key contributions include: (1) a random quantum program generator that produces code with dead code based on quantum control-flow structures, and (2) an adaptation of the EMI technique from classical compiler testing to generate variants by removing dead code. By comparing the behavior of these variants, we can detect potential bugs in QSS implementations. We applied QEMI to Qiskit, Q#, and Cirq, and successfully identified 11 crash bugs and 1 behavioral inconsistency. QEMI expands the limited set of testing techniques available for quantum software stacks by going beyond structural transformations and incorporating semantics-preserving ones into quantum program analysis.
Over the past few years, several quantum software stacks (QSS) have been developed in response to rapid hardware advances in quantum computing. A QSS includes a quantum programming language, an optimizing compiler that translates a quantum algorithm written in a high-level language into quantum gate instructions, a quantum simulator that emulates these instructions on a classical device, and a software controller that sends analog signals to a very expensive quantum hardware based on quantum circuits. In comparison to traditional compilers and architecture simulators, QSSes are difficult to tests due to the probabilistic nature of results, the lack of clear hardware specifications, and quantum programming complexity.This work devises a novel differential testing approach for QSSes, named QDiff with three major innovations: (1) We generate input programs to be tested via semantics-preserving, source to source transformation to explore program variants. (2) We speed up differential testing by filtering out quantum circuits that are not worthwhile to execute on quantum hardware by analyzing static characteristics such as a circuit depth, 2-gate operations, gate error rates, and T1 relaxation time. (3) We design an extensible equivalence checking mechanism via distribution comparison functions such as Kolmogorov–Smirnov test and cross entropy.We evaluate QDiff with three widely-used open source QSSes: Qiskit from IBM, Cirq from Google, and Pyquil from Rigetti. By running QDiff on both real hardware and quantum simulators, we found several critical bugs revealing potential instabilities in these platforms. QDiff’s source transformation is effective in producing semantically equivalent yet not-identical circuits (i.e., 34% of trials), and its filtering mechanism can speed up differential testing by 66%.
As quantum computing transitions from theoretical concepts to commercially available quantum processing units, ensuring the quality, reliability, and correctness of quantum software systems has become paramount. The unique challenges of quantum software testing have necessitated the adaptation of classical software engineering techniques to the quantum domain. One such technique is fuzz testing, or fuzzing, an automated software testing technique that generates large volumes of inputs to identify bugs and unexpected behaviors. In this work we provide a comprehensive examination of how fuzz testing has been successfully applied to quantum computing. We analyze the application of fuzzing across the quantum ecosystem, from testing quantum programs to verifying quantum software stacks, quantum compilers, and quantum simulators. This survey establishes the foundation for understanding how fuzz testing can ensure the reliability and correctness of quantum software systems and outlines promising future research directions.