Abstract
A game-semantics foundation for quantum computation is presented. It draws on two lines of work: for its temporal dynamics, on concurrent games and strategies, based on event structures; 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.
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