Toffoli Gate Using Two-Qubit Gates

Name root sigma x, rsx in qgates.h  library
The first input is the control input, like cnot.
This is a controlled rotation, thus matrix is:

|1+0i  0     0       0     |
|0     1+0i  0       0     | = rsx
|0     0    .5+.5i  .5-.5i |
|0     0    .5-.5i  .5+.5i |

conjugate transpose, rsxt is
|1+0i  0     0       0     |
|0     1+0i  0       0     | = rsxt
|0     0    .5-.5i  .5+.5i |
|0     0    .5+.5i  .5-.5i |

Using kets, |x> = (a+bi)|0> + (c+di)|1> = vector |a+bi c+di|
|0> = vector |1 0| by definition, called a "pure" ket
|1> = vector |0 1|
input |0>|0> = |00> = |1 0 0 0|  input state (tensor product)

output state = rsx * input state
|00> = rsx * |1 0 0 0| = |1 0 0 0| = |00> = |0>|0>
|01> = rsx * |0 1 0 0| = |0 1 0 0| = |01> = |0>|1>
|10> = rsx * |0 0 1 0| = |0 0 .5+.5i  .5-.5i | = |1>|.5+.5i  .5-.5i>
|11> = rsx * |0 0 0 1| = |0 0 .5-.5i  .5+.5i | = |1>|.5-.5i  .5+.5i>
                           state                   kets


Toffoli circuit, X is cnot

a ----. -------------.-----------.----- a
      |              |           |
      |              |  b1       |
b ------------.------X-----.-----X----- b2  should be just b
      |       |            |
      |   c1  |   c2       |
c ---rsx-----rsx----------rsxt--------- cout  should be same as Toffoli

See don_t.cpp     for program source of simulation
See don_t_cpp.out for program simulation output