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Softw. Eng. Methodol."],"published-print":{"date-parts":[[2024,1,31]]},"abstract":"<jats:p>The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Existing work has formulated differentiable quantum programming with bounded loops, providing a framework for scalable gradient calculation by quantum means for training quantum variational applications. However, promising parameterized quantum applications, e.g., quantum walk and unitary implementation, cannot be trained in the existing framework due to the natural involvement of unbounded loops. To fill in the gap, we provide the first differentiable quantum programming framework with unbounded loops, including a newly designed differentiation rule, code transformation, and their correctness proof. 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