I have a large matrix , with elements somewhere between 0 and 0.4 . I want to apply local unitaries, that is, unitary matrices of the form:
$$U_{L} = U \otimes U \otimes U$$
in order to make my matrix contain as many elements equal to zero as possible. In other words, I want to input a somewhat uniform matrix $M$ (all elements are complex and somewhat close), into
$$M' = U_L M U^{\dagger}_L$$
and obtain some large elements and the rest (actually most of the matrix's elements) to be zero.
I have tried doing this by numerically minimizing a few functions over the matrix, like the sum of its elements, the sum of the 4th powers of its elements, sum of absolute values of its elements, but every time the problem is the same. All elements become smaller, but the matrix is still uniform.
Could you suggest a function (somewhat similar to the examples above) that would favor some elements and send the rest to zero?