Valiron, Benoit2013-11-072013-11-0720042004Source: Masters Abstracts International, Volume: 43-06, page: 2254.http://hdl.handle.net/10393/26790http://dx.doi.org/10.20381/ruor-18372The objective of this thesis is to develop a functional programming language for quantum computers based on the QRAM model, following the work of P. Selinger (2004) on quantum flow-charts. We construct a lambda-calculus without side-effects to deal with quantum bits. We equip this calculus with a probabilistic call-by-value operational semantics. Since quantum information cannot be duplicated due to the no-cloning property, we need a resource-sensitive type system. We develop it based on affine intuitionistic linear logic. Unlike the quantum lambda-calculus proposed by Van Tonder (2003, 2004), the resulting lambda-calculus has only one lambda-abstraction, linear and non-linear abstractions being encoded in the type system. We also integrate classical and quantum data types within our language. The main results of this work are the subject-reduction of the language and the construction of a type inference algorithm.124 p.enMathematics.Computer Science.Thesis