Compiling Quantum Conditionals in a Functional Language

Abstract

We present the functional quantum programming language Signe. The language features type inference, quantum conditionals, and compiles to multiple low-level representations. A compiler for Signe is presented with an implementation in Haskell. The compiler uses a Hindley-Milner type system, linearity checking, compilation to circuit and matrix data types, and a modern, user-friendly syntax in the functional style. The operational semantics are described in terms of the category of finite quantum computations FQC. Signe’s semantics and the FQC category are based on the QML language by Altenkirch and Grattage [1, 5, 4].