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LFCS seminar: Glynn Winskel: From probabilistic to quantum strategies

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  • LFCS Seminar
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When Oct 01, 2019
from 04:00 PM to 05:00 PM
Where G.03
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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.)

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