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.

翻译：我们提出了一种名为FOQ的一阶量子编程语言，其终止程序是可逆的。我们将FOQ限制为一个严格且可处理的子集，称为PFOQ，该子集包含具有有界宽度的终止程序，从而首次提供了基于编程语言的量子复杂度类FBQP的刻画。最后，我们提出了一种可处理的、保持语义的算法，可将PFOQ程序编译为规模与输入量子比特数成多项式关系的量子电路。