Circuit description languages are a class of quantum programming languages in which programs are classical and produce a description of a quantum computation, in the form of a quantum circuit . Since these programs can leverage all the expressive power of high-level classical languages, circuit description languages have been successfully used to describe complex quantum algorithms, whose circuits, however, may involve many more qubits and gate applications than current quantum architectures can actually muster. In this article, we present Proto-Quipper-R , a circuit description language endowed with a linear dependent type-and-effect system capable of deriving parametric upper bounds on the width of the circuits produced by a program. We prove both the standard type safety results and that the resulting resource analysis is correct with respect to a big-step operational semantics. Lastly, we introduce QuRA , a static analysis tool based on Proto-Quipper-R ’s type system, and use it to show that our framework allows for the automatic width verification of realistic quantum algorithms, such as the QFT and Grover’s algorithm.

@article{paperbot3309,
  title = {Circuit Width Estimation via Effect Typing and Linear Dependency},
  author = {Andrea Colledan and Ugo Dal Lago and Niki Vazou},
  journal = {ACM Transactions on Programming Languages and Systems},
  volume = {47},
  number = {3},
  year = {2025},
  doi = {10.1145/3737282}
}