  We propose a concept of quantum extensive-form games, which is a quantum
extension of classical extensive-form games. Extensive-form games is a general
concept of games such as Go, Shogi, and chess, which have triggered the recent
AI revolution, and is the basis for many important game theoretic models in
economics. Quantum transitions allow for pairwise annihilation of paths in the
quantum game tree, resulting in a probability distribution that is more likely
to produce a particular outcome. This is similar in principle to the mechanism
of speed-up by quantum computation represented by Grover's algorithm. A quantum
extensive-form game is also a generalization of quantum learning, including
Quantum Generative Adversarial Networks. As an new example of quantum
extensive-form games, we propose a quantum form of the Angel problem originally
proposed by Conway in 1996. The classical problem has been solved but by
quantizing it, the game becomes non-trivial.

Quantum Physics