Towards a quantum programming language

TLDR

Quantum algorithms are typically expressed at the hardware level, such as quantum circuits or Turing machines, which discourages structured programming and abstractions like data types. The paper proposes a quantum programming language that offers high‑level features such as loops, recursion, and structured data types. The language is functional, statically typed, free of run‑time errors, and its denotational semantics are defined using complete partial orders of superoperators.

Abstract

We propose the design of a programming language for quantum computing. Traditionally, quantum algorithms are frequently expressed at the hardware level, for instance in terms of the quantum circuit model or quantum Turing machines. These approaches do not encourage structured programming or abstractions such as data types. In this paper, we describe the syntax and semantics of a simple quantum programming language with high-level features such as loops, recursive procedures, and structured data types. The language is functional in nature, statically typed, free of run-time errors, and has an interesting denotational semantics in terms of complete partial orders of superoperators.