Linear-algebraic lambda-calculus

Abstract

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, $\lambda$-calculus, quantum logics.

LaTeX, 23 pages, 10 figures and the LINEAL language interpreter/simulator file (see "other formats"). See the more recent arXiv:quant-ph/0612199

References in corpus (4)

• A Lambda Calculus for Quantum Computation
• On Quantum Operations as Quantum States
• A 2 rebit gate universal for quantum computing
• Quantum Computation, Categorical Semantics and Linear Logic

Cited by in corpus (4)

• Lineal: A linear-algebraic Lambda-calculus
• Programming Telepathy: Implementing Quantum Non-Locality Games
• Programming with Quantum Communication
• Change actions: from incremental computation to discrete derivatives