This Project generates tilemaps using quantum computing. It uses a set of sample tiles and tilemaps and generates new tilemaps that are similar. The generation algorithm is based on the Wavefunction Collapse Algorithm.
First, we represent our problem as a quadratic unconstrained binary optimization (QUBO) using a sample set of tilemaps. The QUBO is then solved on D-Wave's Quantum Annealer using Ocean SDK
The objective function is a function of binary variables that represent qubits. We will represent our objective function as QUBO which would be used to generate new tilemaps.
Let numMaps be the number of sample maps.
Let numTiles be the number of tiles.
Let numRows be the number of rows in a tilemap.
Let numColumns be the number of columns in a tilemap.
Let,
Where,
the value is 1 if tile t is present at row r and column c in sample map i.
AllowedTop is the set of all pairs of tiles where 2nd tile is allowed to be on top of the first tile
AllowedLeft is the set of all pairs of tiles where 2nd tile is allowed to be on the left of the first tile
AllCombinations is the set of all possible pairs of tiles.
NotAllowedTop is the set of all pairs of tiles where 2nd tile is not allowed to be on top of the first tile.
NotAllowedLeft is the set of all pairs of tiles where 2nd tile is not allowed to be on the left of the first tile.
The Objective Function can then be defined as:-
To represent the Objective Function as QUBO, it needs to be simplified.
We know that,
So, the Objective Function can be simplified as:-
In this example, there are 9 tiles and a set of 5 sample maps with 10 rows and 10 columns.
In this example, there are 40 tiles and a set of 1000 sample maps with 10 rows and 10 columns.
Following are some of the tiles from the set of 40 tiles.
Following are some of the sample maps from the set of 1000 sample maps.
