Generate conditions for the ds parameters, as per QW paper. See also https://github.com/lucainnocenti/QSE-with-QW-code.

QW-for-QSE_conditions_on_ds.m

(* Create the expressions that must be satisfied by the d_s coefficients to generate a specific target
   state after the coin is projected onto the + state. *)
generateConditionsForDs[n_, s_] := Sum[
    Conjugate[u[i] - d[i]] (u[i + n - s] - d[i + n - s]) + Conjugate[d[i + 1]] d[i + n - s + 1],
    {i, 1, s}
] /. {d[1] -> 0, d[n + 1] -> u[n + 1]};