An overview of QML with a concrete implementation in Haskell

TL;DR

This paper provides an overview of the functional quantum programming language QML, including its syntax, semantics, and a Haskell implementation of a compiler that translates QML programs into various quantum representations.

Contribution

It introduces the syntax, semantics, and a practical Haskell compiler for QML, a functional quantum programming language, with a new quantum teleport algorithm implementation.

Findings

Defined QML syntax and semantics including categorical and denotational models

Implemented a Haskell compiler translating QML to quantum circuits, isometries, and superoperators

Discussed orthogonality judgments and coproduct challenges in QML

Abstract

This paper gives an introduction to and overview of the functional quantum programming language QML. The syntax of this language is defined and explained, along with a new QML definition of the quantum teleport algorithm. The categorical operational semantics of QML is also briefly introduced, in the form of annotated quantum circuits. This definition leads to a denotational semantics, given in terms of superoperators. Finally, an implementation in Haskell of the semantics for QML is presented as a compiler. The compiler takes QML programs as input, which are parsed into a Haskell datatype. The output from the compiler is either a quantum circuit (operational), an isometry (pure denotational) or a superoperator (impure denotational). Orthogonality judgements and problems with coproducts in QML are also discussed.