Quantum Recursive Programming with Quantum Case Statements

TL;DR

This paper presents a new quantum recursive programming scheme utilizing quantum case statements, enabling elegant expression of quantum algorithms through recursive definitions and formal semantics.

Contribution

It introduces a novel quantum recursion framework with quantum case statements and a supporting programming language, expanding quantum programming capabilities.

Findings

Quantum recursive programming scheme is introduced.

A simple language supporting quantum recursion is defined.

Examples demonstrate elegant quantum algorithm expressions.

Abstract

We introduce a novel scheme of quantum recursive programming, in which large unitary transformations, i.e. quantum gates, can be recursively defined using quantum case statements, which are quantum counterparts of conditionals and case statements extensively used in classical programming. A simple programming language for supporting this kind of quantum recursion is defined, and its semantics is formally described. A series of examples are presented to show that some quantum algorithms can be elegantly written as quantum recursive programs.