The toric code is a basic computational model as follows:
There are 2 operations that can be performed, A and B, on this grid.
To compute the value A at each point on the grid, we transform the raw values at each dot (located in between two vertices) according to some predefined operators $f_a$ and $f_b$, and multiply the four surrounding values from the operations:
$$ A = f_a(left) f_a(up) f_a(right) f_a(down) $$ $$ B = f_b(left) f_b(up) f_b(right) f_b(down) $$
This seems to be a straightforward question, but I could no find a clear answer anywhere.
What confuses me is what type of quantity is prescribed at each dot, be it a scalar $0.24$, or a complex number $0.24 + 0.12 i$, or a vector $[0.24, 0.12]$?
Also what is the form of the operator function $f_a$ and what is $f_b$, be they 2x2 matrices, or something else?