QuantumChess

Quantum Chess (stylised as Qhess) is a chess variant with a key change: The type of each piece is uncertain and set by it's actions through gameplay.

Whilst sharing some similarities with SpyChess (enough that a computer based implementation of either would be pretty close to being an implementation of the other), it was arrived at independently. Quantum Chess idea is through the grapevine, heard by Nemo via Thomas, and written by here after a discussion about how it would go.

Note: Proto-idea All imagined so far. No actual play testing

Nemo - 2023Nov26

Gameplay

UI mockup

The board is setup as per normal chess - two rows of 8 pieces. However the capability of anyone piece is yet to be determined. Each starting piece has the potential to become any piece, but in doing so, collapses it's options down to that one type, and collapses other pieces options likewise, with the end state being that a traditional chess demographic of pieces is arrived at.

Thus, at the start of the game, every piece has the potential to move in any manner at all. But if a piece moves as a knight, then it can only ever be a knight thereafter. "knightness" is still available to all other pieces. As soon as a second piece is locked in as a knight, no other piece can become a knight. Likewise a piece that moves one space forward may be a pawn, a rook, a king or a queen - but no longer has the opportunity to become a bishop or a knight. If it then moves two spaces sideways, it has further collapsed it's waveform to only include rook and queen possibilities. A piece that moves multiple places diagonally (and has never shown non-diagonal movement) is reduced to being bishop or queen, and the other bishop is only available to pieces that have only moved diagonally on the opposite colour).

These possibilities are visible to both players at all times. In traditional chess, a turn is one step:

1. move a piece (with a requirement to resolve check if it exists).

In quantum chess, a turn is multiple steps:

1. Resolve check (which may be a declaration that an potential-check is not check because the threatened piece is not a king - thus collapsing it's waveform, or may involve moving a piece (this does not prove an potential-check was actual-check. The only collapsed waveforms, if any, are due to piece movement.
2. Move a piece (unless a piece was moved in the previous resolution stage)
3. Declare potential check (if the player chooses to do so - only if one of their pieces has the ability amongst it's options to challenge a could-be-king on the opposite site.

I note here that declaring potential check may involve collapsing waveform of the attacking piece to allow it to make such an attack, but resolving check involves no such collapse, even if the resolution is acted in a way that implies the piece WAS king. Because of these three steps, and the multiple-waveform nature of all pieces, it means at the start of the game the front row is full of potential queens, and also potential kings. A call of potential-check may be made at the start of the game (by collapsing the attacking piece to queen/rook/bishop to do so, depending on the exact target being queried.

The traditional chess "first move" is white. In quantum chess, the first *physical move* is still white, but the first action is in fact a "declare potential check" from black. This (like all potential potential-check checks (golly I enjoyed writing that)) is optional on the players behalf. Black may prefer to not collapse the waveform of any pieces by such a check, meaning white's first turn has no resolve and can go straight to "move a piece".

Castling

This is allowed, and collapses both the king and a rook completely.

Rule based on that of Fisher random chess: ie, both must be on the back row, not have previously moved, and all squares involved must be free from attack, and all square between must be empty. Final positions are as per Fisher random. King/Queen side castling is determined by the relative positions of the rook and king in question.

Fisher Random Chess requires the king to be between the two rooks on initial setup. That requirement does not exist here as the pieces are in superposition, and the original location of the non-castled rook may not be known till later in the game (if at all)

Promotion

This might be tricky, and almost definitely going to require notation update

Taking pieces

A piece is taken as per normal chess - an attacking piece moves into the location of the defeated piece which is then removed off the board.

Some notes:

• taking of a piece does not inherently collapse it's waveform, with the exception it can no longer be a potential King, which may cause a chain reaction of other collapses.
• en passant reveals the attacking piece as a pawn, and is valid against any potential pawn (in a situation where en passant is possible), and thus collapsing it's waveform to a pawn upon capture.

Check and Checkmate

To set the logic here: in regular chess, check is a situation where a king is under attack (ie, if it were a normal piece, it could be taken next turn), and the player of that king MUST in their turn resolve that situation so as to not be in check. If that is impossible, then it is checkmate.

In Qhess, the same basic logic applies, but needs to be explained to cover superpositions.

• potential-check is a situation where a potential-king is under attack. This ONLY occurs by declaration of the attacking player (it is never automatic), and has three possible resolutions
  • Defending player declaring that it wasn't a king afterall. Defending player still has a physical turn.
  • Defending player moves another piece to defend the potential-king. This may collapse the waveform of the moved piece, but does not collapse that of the potential-king. They may yet turn out to not be the king
  • Defending player moves the potential-king piece out of the way, and if appropriate to it's movement, its waveform collapses as per normal waveform collapse behaviour.
• automatic check is akin to traditional chess - where a singular king is under attack by a piece with the capability to do so (even if it has other waveforms available to it). However, due to the superposition nature of pieces, a hypothetical situation is that a players turn begins with two potential-kings, both under attack one is challenged by potential-check, and the defending player defends in a way that collapses the potential-check by declaring that piece not-king. The other potential-king now collapses to be the true king and is under attack = check (automatically)

Checkmate is as per regular chess - a situation where the king cannot move out of check. A checkmate cannot occur with multiple potential kings, since the base logic of checkmate is "I will take your king on my next turn", but if there are multiple potential-kings, then the true king cannot be definitively identified.

Implementation

It's very likely that this is best implemented in computer, where each piece's waveform options can not only be easily visualised, but visual filters for waveform options can be applied easily, as well as predictive "if I move this piece and collapse it's waveform in a certain way, what other waveform collapses occur?". It is imagined that each of the six piece types be represented by a colour, and each piece thus be a grid or a pie-chart to show the waveforms it's still unclear on. (if needed, the border of the pie chart in black/white to denote which side they're on)

A physical implementation may be done with Trivial Pursuit pieces, however collapsing waveforms by hand may be difficult, due to chained collapses (eg: if two pieces are Rook/Queens, and one collapses to the Queen, the other collapses to a Rook) and implicit collapses (eg: if three pieces are, respectively, Queen/BlBishop/Pawn, Queen/BlBishop and Queen/BlBishop and no other pieces have Queen/BlBishop available to them, then the first collapses to a pawn, since otherwise two bishops or two queens are inevitable). Iterating recursively through all collapse options after every collapse is liable to be tedious and error prone.

Notation

Qhess notation is derived from chess algebraic notation, and intended (not proven) to be both unambiguous, and to itself collapse to standard algebraic notation.

Chess algebraic notation normally uses an indicator of the type of piece, plus the minimum of disambiguation required, and then the destination coordinate. Long algebraic notation gives from source and destination coordinates. Qhess aims to use long algebraic notation at it's core. Long algebraic notation is (apparently) also commonly used in UCI for communication between engine and interface, and our notation here will intend to be used the same way

Additions to the standard:

• (optional) specifying the waveforms of a piece BEFORE it's location. The letter codes are as per english chess algebraic notation, with the addition of 'P' for Pawn. If there are multiple letters, they are held within parenthesis. eg: (KQBNRP)e2
• Specifying the waveform of a piece at it's location - this indicates a specification of it's waveform state. This (alongside with colour indication, see below) may be used to save/restore the state of a board midgame, resolve potential-check challenge, or (optionally) be used to indicate waveform collapse at the end of a piece's movement eg: e4(QRP). it is presented in square brackets for the first two cases (this is a nod to Portable Game Notation for initialisation of mid-game boards)
• (optional) specifying the colour of a piece with "b_" or "w_" preceeding the first-displayed waveform state of a piece at it's location. Like most of algebraic notation, it's only included when required for disambiguation. If the notation is for a game from the start, then it is never needed. However if the notation is restoring a saved gamestate, then it is needed on initialisation of the board. eg: e4(b_QRP)
• A move may be as simple as long algebraic notation with no additions "e2e4" or may include the full waveform specifications "(b_KQBNRP)e2e4(QRP)"
• A potential-check challenge is written as a sequence of positions within angle brackets, with 1..(n-1) being attacking pieces (there may be multiple, with waveform collapse stated as needed), and the nth position being the target. eg, this would be a valid opening move "<(w_KQBNRP)g2(QR) (w_KQBNRP)b2(QB) g7>", and could be written at bare minimum as <g2 b2 g7>
• Normal (definite) check is still indicated by a "+" same as normal
• move zero is allowed for the initial black potential-check challenge, should they choose to play it.

Once a piece collapses to a single type, it no longer needs to be in brackets, and no longer needs to specify it's source location (beyond disambiguation needs). This the base notation collapses to standard algebraic notation.

thus a game progress is (each turn being white, then black):

   0... <challenge>
   1. [resolve] move <challenge> [resolve] move <challenge>
   2. [resolve] move <challenge> [resolve] move <challenge>
   3. move move

etc. "[resolve]" and "<challenge>" information are optional - they are not part of every turn.

Note: these additions are not rigorously thought through!

Useful links:

• https://en.wikipedia.org/wiki/Algebraic_notation_(chess)
• https://en.wikipedia.org/wiki/Portable_Game_Notation
• https://en.wikipedia.org/wiki/Universal_Chess_Interface

See also

SpyChess also written up on this wiki is an older chess variant which shares the similarity that the types of each opponent's piece is unknown and is discovered through gameplay. However in Spy Chess, a piece's type is definitively known to their own side at the start of the game. Quantum Chess differs in that a type isn't definitively known, and a player can choose what each piece becomes throughout the game.