Semantic Abstraction and Quantum Computation

Semantic Abstraction and Quantum Computation

We present a logico-algebraic approach to probabilistic abstract interpretation based on the ortholattice structure of the projective measurement operators in quantum mechanics. On this base, we present a novel interpretation of quantum measurement as a probabilistic abstraction showing that the measurement of a physical observable essentially corresponds to a static analysis of the observed pr...

Geometry of abstraction in quantum computation

Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke and Selinger. In particular, we analyze function abstraction in quantum computation, which turns out to characterize its classical interfaces. Intuitively, cla...

Semantic Techniques for Quantum Computation

Computing Science Group Geometry of abstraction in quantum computation

Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke and Selinger. In particular, we analyze function abstraction in quantum computation, which turns out to characterize its classical interfaces. Some quantum alg...

Semantic Abstraction and Anaphora

This paper describes a way of expressing syntactic rules that ~kssociate semantic formulae with strings, but in a manner thai is independent of the syntactic details of these formulac. In particular we show how the same rules construct predicate argument formulae in the style of Montague grammar[131, rap_ resentations reminiscent of situation semantics(Barwise and Perry 121) and of the event lo...