Talk by Glynn Winskel - From probabilistic to quantum strategies
I'll present a recent games foundation for quantum computation developed with Pierre Clairambault and Marc de Visme. It draws on two lines of work: for its temporal dynamics, on concurrent games and strategies, based on event structures - specifically on probabilistic concurrent strategies; for its quantum interactions, on the mathematical foundations of positive operators and completely positive maps. The two lines are married in the definition of quantum concurrent strategy, obtained via an operator generalisation of the conditions on a probabilistic concurrent strategy.
The result is a compact-closed (bi)category of quantum games, whose finite configurations carry finite dimensional Hilbert spaces, and quantum strategies, whose finite configurations carry operators. Finally I'll indicate how the quantum concurrent strategies relate to a form of synchronising quantum circuit based on Petri nets.
Glynn Winskel is professor at University of Cambridge Computer Laboratory and Turing Fellow at The Alan Turing Institute. He was awarded an Advanced Grant by the European Research Council 'Events, Causality and Symmetry---the next generation semantics' in 2011. Also, he is a member of the Academia Europaea.
He is probably best known for his work generalising the methodology of domain theory and denotational semantics to concurrent computation, and as the main developer of event structures. He sees his research as developing the mathematics with which to understand and analyze computation, its nature, power and limitations. Computation today is highly distributed and interactive, often probabilistic, and sometimes based in quantum theory or biology. Traditional models fall short: they are either too low level (as with 'Turing machines') or have abstracted too early from operational and quantitative concerns (the case with domain theory, the classical foundation of denotational semantics). His distributed games arguably provide the most versatile foundation for denotational semantics we have.