Alice Wismath, a computer science student at Queen's University in Canada, has developed a form of chess in which the type of a given piece on the board is in a state of flux:
Link via Marginal Revolution | Photo by Flickr user soupboy used under Creative Commons license
In the quantum chess computer game created by undergraduate computer science student Alice Wismath, a piece that should be a knight could simultaneously also be a queen, a pawn or something else. The player doesn't know what the second state might be or which of the two states the piece will choose when it is moved.[...]
Wismath also chose new rules to make the game workable with its quantum twist. For example, her version of quantum chess requires a player to capture the king, which never changes to another piece, instead of merely delivering a checkmate. Also, pieces change states only when they land on black squares.
Link via Marginal Revolution | Photo by Flickr user soupboy used under Creative Commons license
But if you've got him in checkmate, your next move is to take the king, and that would be the end of the game, no matter what the piece turns into after you've moved.
No need to make the game so complicated, though. Seems kinda silly.
BTW there was a 'fake advertisement' for Quantum Chess in Games Magazine years ago.
So basically, the bishops on white squares are non-quantum?