Added a shift to colswap in _perform_row_operations

[manuelgpda]

When performing operations on the bimatrices of Code objects for finding the standard form one needed to take into account the shift given by start_row. This comes from the fact that first, one finds the rref of the left sub matrix A and then the rref of the right sub sub matrix E. After finding A, one needs to shift the row operations we are performing a number of start_row=self.rankx elements to the right so one does not mess with the identity that is on the left already and this was implemented in the code as it should. However, one should also shift the column operations in order to avoid messing with the aforementioned identity and this was not considered in the code.

I don't believe though that this sole change will fix #2 .

[abdullahkhalids]

Thank you. Does this fix encoding for the codes in the notebook linked in issue #2 ?

[manuelgpda]

I think that this does not fix #2 but I have not checked in depth.

[abdullahkhalids]

I agree that this is likely a correct partial fix to the algorithm. But I would like some justification. Did you try it with any code, where the change improved things?

[manuelgpda]

Yes, if you try:

def get_generator_matrix(stabilisers):
    generator_matrix_list = []
    for jj,stab in enumerate(stabilisers):
        row = [0]*2*len(stab)
        for ii,letter in enumerate(stab):
            if letter == 'X':
                row[ii] = 1
            if letter == 'Z':
                row[len(stab) + ii] = 1
            if letter == 'Y':
                row[ii] = 1
                row[len(stab) + ii] = 1
        generator_matrix_list.append(row)
    return np.array(generator_matrix_list)

generators = ['IYZXIIIXZYII', 'IXZYIIIYZXII']
gm = get_generator_matrix(generators)
cd_rep = stac.Code(gm)
st = cd_rep.construct_standard_form()
print('r:',cd_rep.rankx)
print('X submatrix:')
print(st[0])
print('Z submatrix:')
print(st[1])

The output will be:

r: 1
X submatrix:
[[0 0 1 1 0 0 0 1 0 1 0 0]
 [0 0 0 0 0 0 0 0 0 0 0 0]]
Z submatrix:
[[1 0 1 0 0 0 0 0 1 1 0 0]
 [0 0 1 1 0 0 0 1 0 1 0 0]]

And this makes no sense since r=1 implies that the X sub matrix has to have an identity sub matrix of size 1x1 and the very left. However, after implementing #3 , the output will be:

r: 1
X submatrix:
[[1 1 0 0 0 0 0 1 0 1 0 0]
 [0 0 0 0 0 0 0 0 0 0 0 0]]
Z submatrix:
[[1 0 1 0 0 0 0 0 1 1 0 0]
 [1 1 0 0 0 0 0 1 0 1 0 0]]

[abdullahkhalids]

Excellent. This looks correct. I will accept this in a couple of weeks, because I am in the middle of teaching a workshop that uses stac, and there will be some confusion.

Thanks for the contribution.

[abdullahkhalids]

Thanks.