Formal Quantum Software Engineering: Introducing the Formal Methods of Software Engineering to Quantum Computing

Abstract: Quantum computing (QC) represents the future of computing systems, but the tools for reasoning about the quantum model of computation, in which the laws obeyed are those on the quantum mechanical scale, are still a mix of linear algebra and Dirac notation; two subjects more suitable for physicists, rather than computer scientists and software engineers. On this ground, we believe it is possible to provide a more intuitive approach to thinking and writing about quantum computing systems, in order to simplify the design of quantum algorithms and the development of quantum software. In this paper, we move the first step in such direction, introducing a specification language as the tool to represent the operations of a quantum computer via axiomatic definitions, by adopting the same symbolisms and reasoning principles used by formal methods in software engineering. We name this approach formal quantum software engineering (F-QSE). This work assumes familiarity with the basic principles of quantum mechanics (QM), with the use of Zed (Z) which is a formal language of software engineering (SE), and with the notation and techniques of first-order logic (FOL) and functional programming (FP).