#OK to post homework
#Joseph Koutsoutis, 03-30-2025, Assignment 16

read `QC.txt`:
read `C16.txt`:

#2

ToffoliMatrix := proc() local T:
  T[[0,0,0]] := [0,0,0]:
  T[[0,0,1]] := [0,0,1]:
  T[[0,1,0]] := [0,1,0]:
  T[[0,1,1]] := [0,1,1]:
  T[[1,0,0]] := [1,0,0]:
  T[[1,0,1]] := [1,0,1]:
  T[[1,1,0]] := [1,1,1]:
  T[[1,1,1]] := [1,1,0]:
  TtoUM([T, BV(3)], 3):
end:


FredkinMatrix := proc() local T:
  T[[0,0,0]] := [0,0,0]:
  T[[0,0,1]] := [0,1,0]:
  T[[0,1,0]] := [0,0,1]:
  T[[0,1,1]] := [0,1,1]:
  T[[1,0,0]] := [1,0,0]:
  T[[1,0,1]] := [1,0,1]:
  T[[1,1,0]] := [1,1,0]:
  T[[1,1,1]] := [1,1,1]:
  TtoUM([T, BV(3)], 3):
end:


#3

Sjk := proc(j,k):
  [[1, 0, 0, 0],
   [0, 1, 0, 0],
   [0, 0, 1, 0],
   [0, 0, 0, exp(I*Pi / 2^(k-j))]]:
end:


#4

QFTC := proc(l) local C, j, k:
  C := []:
  for j from l-1 to 0 by -1 do:
    for k from l-1 to j+1 by -1 do:
      C := [op(C), [[j, k], Sjk(j, k)]]:
    od:
    C := [op(C), [[j], C1QG()[7]]]:
  od:
  [l, C]:
end: