Quantum Register Machine: Efficient Implementation of Quantum Recursive Programs

TL;DR

This paper introduces a quantum register machine architecture that enables efficient implementation of quantum recursive programs, supporting quantum control flow and recursion, and achieving automatic parallelisation with exponential speed-up for certain algorithms.

Contribution

It presents the first quantum register machine with instruction-level support for quantum recursion and control flow, along with a comprehensive implementation process and automatic parallelisation techniques.

Findings

First quantum architecture supporting quantum recursion and control flow

Implementation process including compilation and execution on the quantum register machine

Automatic parallelisation yields exponential speed-up for certain quantum algorithms

Abstract

Quantum recursive programming has been recently introduced for describing sophisticated and complicated quantum algorithms in a compact and elegant way. However, implementation of quantum recursion involves intricate interplay between quantum control flow and recursive procedure calls. In this paper, we aim at resolving this fundamental challenge and develop a series of techniques to efficiently implement quantum recursive programs. Our main contributions include: 1. We propose a notion of quantum register machine, the first quantum architecture (including an instruction set) that provides instruction-level support for quantum control flow and recursive procedure calls at the same time. 2. Based on quantum register machine, we describe the first comprehensive implementation process of quantum recursive programs, including the compilation, the partial evaluation of quantum control flow, and the execution on the quantum register machine. 3. As a bonus, our efficient implementation of quantum recursive programs also offers automatic parallelisation of quantum algorithms. For implementing certain quantum algorithmic subroutine, like the widely used quantum multiplexor, we can even obtain exponential parallel speed-up (over the straightforward implementation) from this automatic parallelisation. This demonstrates that quantum recursive programming can be win-win for both modularity of programs and efficiency of their implementation.