With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an interpreter/simulator) is provided for this language in the form of a term rewrite system. The linear-algebraic lambda-calculus hereby constructed is linear in a different (yet related) sense to that, say, of the linear lambda-calculus. These various notions of linearity are discussed in the context of quantum programming languages. KEYWORDS: quantum lambda-calculus, linear lambda-calculus, $λ$ -calculus, quantum logics.With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an interpreter/simulator) is provided for this language in the form of a term rewrite system. The linear-algebraic lambda-calculus hereby constructed is linear in a different (yet related) sense to that, say, of the linear lambda-calculus. These various notions of linearity are discussed in the context of quantum programming languages. KEYWORDS: quantum lambda-calculus, linear lambda-calculus, $λ$-calculus, quantum logics.

arXiv:quant-ph/0501150Jan 25, 20057 citations

Quantum process calculus for linear optical quantum computing

Ittoop Vergheese Puthoor

Dec 31, 20130 citations

Quantum Process Calculus for Linear Optical Quantum Computing

Sonja Franke‐Arnold, Simon J. Gay, Ittoop Vergheese Puthoor

Lecture notes in computer scienceJan 1, 201313 citations

λ

-calculus, quantum logics.