  The most promising applications of quantum computing are centered around
solving search and optimization tasks, particularly in fields such as physics
simulations, quantum chemistry, and finance. However, the current quantum
software testing methods face practical limitations when applied in industrial
contexts: (i) they do not apply to quantum programs most relevant to the
industry, (ii) they require a full program specification, which is usually not
available for these programs, and (iii) they are incompatible with error
mitigation methods currently adopted by main industry actors like IBM. To
address these challenges, we present QOPS, a novel quantum software testing
approach. QOPS introduces a new definition of test cases based on Pauli strings
to improve compatibility with different quantum programs. QOPS also introduces
a new test oracle that can be directly integrated with industrial APIs such as
IBM's Estimator API and can utilize error mitigation methods for testing on
real noisy quantum computers. We also leverage the commuting property of Pauli
strings to relax the requirement of having complete program specifications,
making QOPS practical for testing complex quantum programs in industrial
settings. We empirically evaluate QOPS on 194,982 real quantum programs,
demonstrating effective performance in test assessment compared to the
state-of-the-art with a perfect F1-score, precision, and recall. Furthermore,
we validate the industrial applicability of QOPS by assessing its performance
on IBM's three real quantum computers, incorporating both industrial and
open-source error mitigation methods.
