Title: Toward Quantum Combinatorial Games,
Abstract: In this paper, we propose a Quantum variation of combinatorial games,
generalizing the Quantum Tic-Tac-Toe proposed by Allan Goff. A combinatorial
game is a two-player game with no chance and no hidden information, such as Go
or Chess. In this paper, we consider the possibility of playing superpositions
of moves in such games. We propose different rulesets depending on when
superposed moves should be played, and prove that all these rulesets may lead
similar games to different outcomes. We then consider Quantum variations of the
game of Nim. We conclude with some discussion on the relative interest of the
different rulesets.