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Q# is a standalone domain-specific programming language from Microsoft forwriting and running quantum programs. Like most industrial languages, it wasdesigned without a formal specification, which can naturally lead to ambiguityin its interpretation. We aim to provide a formal language definition for Q#,placing the language on a solid mathematical foundation and enabling furtherevolution of its design and type system. This paper presents $\lambda$-Q#, anidealized version of Q# that illustrates how we may view Q# as a quantum Algol(algorithmic language). We show the safety properties enforced by$\lambda$-Q#'s type system and present its equational semantics based on afully complete algebraic theory by Staton.

Q# as a Quantum Algorithmic Language