don_t.cpp running
notation  (x,y) is complex number x+iy
          vectors are printed   vec[j] = (x,y)
          matrices are printed  mat[i][j] = (x,y)

to be a valid qubit, ket notation  a|0> + b|1> 
a^2 + b^2 must equal 1
 a and b are shown as (x,y) x real part, y imaginary part
 a is first element of vector, b is second element of vector
 in computer code and printout

a ket represents a qubit, stored as a vector of two complex numbers
logical zero = |0> = ket0 = a complex column vector
vec[0] = (1,0)
vec[1] = (0,0)

logical one = |1> = ket1 =
vec[0] = (0,0)
vec[1] = (1,0)


just test cnot2 function
the cnot matrix is:
mat[0][0] = (1,0)
mat[0][1] = (0,0)
mat[0][2] = (0,0)
mat[0][3] = (0,0)
mat[1][0] = (0,0)
mat[1][1] = (1,0)
mat[1][2] = (0,0)
mat[1][3] = (0,0)
mat[2][0] = (0,0)
mat[2][1] = (0,0)
mat[2][2] = (0,0)
mat[2][3] = (1,0)
mat[3][0] = (0,0)
mat[3][1] = (0,0)
mat[3][2] = (1,0)
mat[3][3] = (0,0)

cnot |1>|0> =
vec[0] = (0,-0)
vec[1] = (1,-0)
|1>  check |1>

test ccnot3, toffoli function
the ccnot matrix is:
mat[0][0] = (1,0)
mat[0][1] = (0,0)
mat[0][2] = (0,0)
mat[0][3] = (0,0)
mat[0][4] = (0,0)
mat[0][5] = (0,0)
mat[0][6] = (0,0)
mat[0][7] = (0,0)
mat[1][0] = (0,0)
mat[1][1] = (1,0)
mat[1][2] = (0,0)
mat[1][3] = (0,0)
mat[1][4] = (0,0)
mat[1][5] = (0,0)
mat[1][6] = (0,0)
mat[1][7] = (0,0)
mat[2][0] = (0,0)
mat[2][1] = (0,0)
mat[2][2] = (1,0)
mat[2][3] = (0,0)
mat[2][4] = (0,0)
mat[2][5] = (0,0)
mat[2][6] = (0,0)
mat[2][7] = (0,0)
mat[3][0] = (0,0)
mat[3][1] = (0,0)
mat[3][2] = (0,0)
mat[3][3] = (1,0)
mat[3][4] = (0,0)
mat[3][5] = (0,0)
mat[3][6] = (0,0)
mat[3][7] = (0,0)
mat[4][0] = (0,0)
mat[4][1] = (0,0)
mat[4][2] = (0,0)
mat[4][3] = (0,0)
mat[4][4] = (1,0)
mat[4][5] = (0,0)
mat[4][6] = (0,0)
mat[4][7] = (0,0)
mat[5][0] = (0,0)
mat[5][1] = (0,0)
mat[5][2] = (0,0)
mat[5][3] = (0,0)
mat[5][4] = (0,0)
mat[5][5] = (1,0)
mat[5][6] = (0,0)
mat[5][7] = (0,0)
mat[6][0] = (0,0)
mat[6][1] = (0,0)
mat[6][2] = (0,0)
mat[6][3] = (0,0)
mat[6][4] = (0,0)
mat[6][5] = (0,0)
mat[6][6] = (0,0)
mat[6][7] = (1,0)
mat[7][0] = (0,0)
mat[7][1] = (0,0)
mat[7][2] = (0,0)
mat[7][3] = (0,0)
mat[7][4] = (0,0)
mat[7][5] = (0,0)
mat[7][6] = (1,0)
mat[7][7] = (0,0)

ccnot3 all 8 cases of keta, ketb, ketc as |0> and |1>
 inputs   |  outouts 
|a>|b>|c> | |a>|b>|cout>
----------|------------
|0>|0>|0> | |0>|0>|0>
|0>|0>|1> | |0>|0>|1>
|0>|1>|0> | |0>|1>|0>
|0>|1>|1> | |0>|1>|1>
|1>|0>|0> | |1>|0>|0>
|1>|0>|1> | |1>|0>|1>
|1>|1>|0> | |1>|1>|1>
|1>|1>|1> | |1>|1>|0>

test rsx2 function
rsx |0>|0> =
vec[0] = (1,-0)
vec[1] = (0,-0)
|0>

rsx |0>|1> =
vec[0] = (0,-0)
vec[1] = (1,-0)
|1>

rsx |1>|0> =
vec[0] = (0.5,-0.5)
vec[1] = (0.5,0.5)
(0.5,-0.5) |0> + (0.5,0.5) |1>

rsx |1>|1> =
vec[0] = (0.5,0.5)
vec[1] = (0.5,-0.5)
(0.5,0.5) |0> + (0.5,-0.5) |1>


test rsxt2 function
rsxt |0>|0> =
vec[0] = (1,-0)
vec[1] = (0,-0)
|0>

rsxt |0>|1> =
vec[0] = (0,-0)
vec[1] = (1,-0)
|1>

rsxt |1>|0> =
vec[0] = (0.5,0.5)
vec[1] = (0.5,-0.5)
(0.5,0.5) |0> + (0.5,-0.5) |1>

rsxt |1>|1> =
vec[0] = (0.5,-0.5)
vec[1] = (0.5,0.5)
(0.5,-0.5) |0> + (0.5,0.5) |1>


test Don's version of toffoli function

Don's all 8 cases of keta, ketb, ketc as |0> and |1>
 inputs   |  outouts 
|a>|b>|c> | |a>|b>|cout>
----------|------------
|0>|0>|0> | |0>|0>|0>
|0>|0>|1> | |0>|0>|1>
|0>|1>|0> | |0>|1>|0>
|0>|1>|1> | |0>|1>|1>
|1>|0>|0> | |1>|0>|0>
|1>|0>|1> | |1>|0>|1>
|1>|1>|0> | |1>|1>|1>
|1>|1>|1> | |1>|1>|0>

finished don_t.cpp