A brief introduction to quantum chess

Let's talk about the rules in general,

Game state

All the pieces in quantum chess are the same as in classical chess, except that all the pieces in quantum chess can be in superposition, that is, they can occupy more than one square at a time. But according to the concept of quantum superposition, here each occupied square has a different probability, and their total probability sum is 1, and here the probability of the possession of each piece on the board is the probability that if we make a quantum measurement we can get one of the pieces on the board.

Move

The movement rules here are based on the rules given by quantum mechanics, and then the game is much richer, which is that I can move in a superposition, which might be counter-intuitive.

Due to the introduction of quantum rules, there will be several kinds of movement:

Standard movement

Quantum chess follows the rules of the original classical chess, including castling, eating pawns, etc., but with caveats:

1. There is no concept of "general";

2, the pieces in the superposition of the way to occupy the square will not hinder the standard movement. This means that, for example, a knight (horse) can move to a square occupied by a piece on the same side that is in superposition, or a queen can move to a square occupied by a piece that is in superposition.

The "doppelganger" moves

All pieces that are not pawns can make "split body" moves. This move allows the piece to "split" and occupy two different squares, although only squares that are not occupied or are occupied by the same color and type are considered legitimate moving targets. This means that a white knight can "split" to a square occupied by another White knight, which also means that a "split" move cannot capture the opponent's piece.

"Confluent" move

All pieces that are not pawns can make "confluent" moves. This step is the inverse operation of the "dopey" move, again only those occupying two different squares, and of course only the squares that are not occupied or are occupied by the same color and type, are considered legitimate moving targets. This means that two white knights can converge to a square occupied by another white knight. This also means that a confluent move cannot be made to capture the piece.

measure

Any time we move the target in one square at a time, it means we need to see if the square is occupied. This may cause some of the superposition states to collapse so that these pieces are not in superposition. Measurement is introduced here to answer some yes or no decisive answers, since superposition is uncertain, so we need to measure. If the answer is yes, the operation can be performed. If the answer is no, no further action will be taken and this step will be skipped to the opponent player. Note that in this case, of course, the state on the chessboard is still changed due to the collapse of the superposition, and there are two different measurement scenarios to consider.

Capture - "eat"

In the attempt to "eat", the game measures the probability of the square that is being occupied by the moving piece, and for the "split" piece measures the probability of the grid points on all paths occupied by the piece superposition, the measurement answers the question:

Does the piece to attack exist, and can it reach the target position?

Note that if the answer is no, it does not mean that the attacking piece does not exist, nor does it mean that the path is blocked. It could be one or the other, so you need to look at the probability change to reflect that both are more likely

Castling of the chariot

This is a very special operation, the castling involves two target positions, so we need to measure at both positions. Castling cannot be used to capture pieces.

Special movement

If a moving object is occupied in a superposition state, the piece cannot be captured by this move, we call it a special move. In this case, the game needs to measure the target square. For sliding pieces, any square in the path from the beginning square to the target square occupied by the pieces in a superposition state needs to be measured. The measurement here needs to answer the question:

Is the target square empty and can the moving piece reach it?

Note that if the answer is no, it does not mean that the target square is occupied, nor does it mean that the path is blocked. It could be one of the reasons, so you can see that the change in probability is more likely in both cases.

win

The way to win the game is to "eat" the opponent's king. This means that the opponent has no king anywhere on the board. For any piece, including the king, there may be a superposition of "eaten" and not "eaten". Only when you are absolutely certain that your opponent does not have a king, then you win!

Of course, it is also possible for both players to lose the king at the same time, which would be a draw.

We follow the game guide to introduce, first given an 8 by 8 board,

If you have a piece on the board, like the knight given here,

Just like the classic game we can do the standard move, there will be eight positions to move,

Next, the new rules of play,

The "doppelganger" move allows you to select two different locations,

If we choose any two positions out of eight, this is equivalent to the evolution of one state and the choice we make is equivalent to the evolution matrix,

So you can see that this knight can be in superposition, but these two positions have a probability of being in these two positions, because it's not definite, that is, superimposed together,

But you can't capture your opponent's piece in this step, your piece can be eaten by your opponent,

Because it's in a superposition state, we don't know if our placed "dopes" are captured until we start measuring,

And while two different pieces can't occupy the same square, we need to measure which square the pieces are actually on,

If in the "doppelganger" state, we think about "eating son,"

The knight here can eat the pawn in position A5, but because the pieces are in superposition, this position is uncertain, it's superimposed, so at this point we need to measure to determine whether this knight is really in position B3 or C2, and unfortunately, after we measure it, it's in position C2, and it's eaten by the opponent's knight. There's another situation where we measure the knight in position B3, and then we can eat the pawn in position A5, and then the superposition comes into play,

If the pieces are in a "split" state, it is possible to "converge" together, this time because of two different "split", when choosing the next position, you can always choose (evolve) to the same position, this time is "confluence".

At this time, choose the location where the two "doppelgangers" meet.

At this point, the basic rules have been stated, and in order to win the game, we need to "eat" the opponent's king, and there is no "general" in quantum chess.

Simple rules have been introduced, just finished learning, need to continue to understand in the future, this aspect of the game and research is really interesting.