A programming language characterizing quantum polynomial time

2022-12-13

Foundations of Software Science and Computation Structure

AI Summary

This work addresses the lack of a precise programming-language-level characterization of the quantum complexity class FBQP. We introduce FOQ, the first first-order quantum programming language, and its restricted subset PFOQ. PFOQ enforces syntactic constraints guaranteeing reversibility, bounded qubit width, and strong termination—thereby capturing exactly the class FBQP. Methodologically, we provide the first programming-language-based semantic characterization of FBQP and design a semantics-preserving, polynomial-size compilation algorithm that automatically translates any PFOQ program into an equivalent quantum circuit whose size is polynomial in the input length. Our main contributions are: (1) the first exact, programmable-language characterization of FBQP; (2) a quantum language design that simultaneously ensures reversibility, guaranteed termination, and static analyzability; and (3) a theoretically sound and practically implementable compilation framework bridging high-level quantum programs and efficient circuit implementations.

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.

Problem

• Characterizing quantum polynomial time computation
• Defining reversible quantum programming language
• Compiling programs to efficient quantum circuits

Innovation

• First-order quantum programming language FOQ
• Reversible terminating programs with bounded width
• Compilation to polynomial-size quantum circuits