A Functional Programming Language for Quantum Computing with Classical Control

Title: A Functional Programming Language for Quantum Computing with Classical Control

Abstract: This research article proposes a higher-order quantum programming language that combines classical and quantum features. The language is designed to operate on both classical and quantum data types, with the control structure encoded in lambda terms, which are implemented classically. The semantics of the language is operational and probabilistic. The main results of this paper are the safety properties of the language and the development of a type inference algorithm based on affine intuitionistic linear logic.

Main Research Question: How can we develop a functional programming language that effectively combines classical and quantum features for quantum computing with classical control?

Methodology: The research team developed a higher-order quantum programming language that encodes the control structure in lambda terms, which are implemented classically. The language operates on both classical and quantum data types, taking advantage of their unique properties. The semantics of the language is operational and probabilistic.

Results: The research team has developed a type system using affine intuitionistic linear logic, which is appropriate for higher-order quantum functions in their setting. They have also developed a type inference algorithm that reduces the question of deciding whether a program is valid to finding an intuitionistic type for it and exploiting a finite number of linear decorations for the type.

Implications: The development of this functional programming language for quantum computing with classical control has significant implications for the field. It provides a practical and efficient way to combine classical and quantum features in a single programming language, which can lead to more advanced and powerful quantum computing systems. Additionally, the type system and type inference algorithm developed in this research can serve as a foundation for further studies and applications in the field.

Link to Article: https://arxiv.org/abs/0404056v2 Authors: arXiv ID: 0404056v2