Towards a Quantum Calculus: (Work in Progress, Extended Abstract)

Progress, Extended Abstract) Philippe Jorrand1 Simon Perdrix2 Leibniz Laboratory IMAG-INPG Grenoble, France The aim of this paper is to introduce a general model of quantum computation, the quantum calculus: both unitary transformations and projective measurements are allowed; furthermore a complete classical control, including conditional structures and loops, is available. Complementary to its operational semantics, we introduce a pure denotational semantics for the quantum calculus. Based on probabilistic power domains [4], this pure denotational semantics associates with any description of a computation in the quantum calculus its action in a mathematical setting. Adequacy between operational and pure denotational semantics is established. Additionally to this pure denotational semantics, an observable denotational semantics is introduced. Following the work by Selinger, this observable denotational semantics is based on density and super-operators. Finally, we establish an exact ...

• Type: Journal
• Year: 2008
• Where: ENTCS
• Authors: Philippe Jorrand, Simon Perdrix
• Keywords: Denotational Semantics, ENTCS 2008, Observable Denotational Semantics, Pure Denotational Semantics