A programming language characterizing quantum polynomial time

TL;DR

This paper introduces FOQ, a quantum programming language, and its subset PFOQ, which characterizes the class FBQP and includes an efficient compilation algorithm to quantum circuits.

Contribution

It defines a new quantum programming language and subset that characterize FBQP, with an algorithm for compiling programs into quantum circuits.

Findings

PFOQ characterizes the class FBQP.

A polynomial-size quantum circuit compilation algorithm is provided.

FOQ ensures reversible terminating programs.

Abstract

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.