We introduce a first-order quantum programming language, named FOQ, whose terminating programs are reversible. We restrict FOQ to a strict and tractable subset, named PFOQ, of terminating programs with bounded width, that provides a first programming language-based characterization of the quantum complexity class FBQP. Finally, we present a tractable semantics-preserving algorithm compiling a PFOQ program to a quantum circuit of size polynomial in the number of input qubits.
Cite
@article{arxiv.2212.06656,
title = {A programming language characterizing quantum polynomial time},
author = {Emmanuel Hainry and Romain Péchoux and Mário Silva},
journal= {arXiv preprint arXiv:2212.06656},
year = {2025}
}