Orthogonality and Algebraic Lambda-Calculus

Directly encoding lambda-terms on quantum strings while keeping a quantum interpretation is a hard task. As shown by van Tonder [2004], requiring a unitary reduction forces the lambda-terms in superposition to be mostly equivalent. Following instead [Arrighi and Dı́az-Caro, 2009], we show in this note how one can conceive a lambdacalculus with algebraic features and that admits a general notion of orthogonality amongst lambdaterms, by providing a compiler of the system into unitary maps.