LFCS Seminar: 1 October 2019 - Glynn Winskel

Title: From Probabilistic to Quantun Stragies

Abstract:

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 bicategory 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 are refined to a form of synchronising quantum circuits based on Petri nets. (Quantum concurrent strategies have recently been shown to yield an intensionally fully-abstract model of the quantum lambda-calculus; the 'quantum Petri nets' were uncovered for an accompanying definability result.)