nand.cpp running

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

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

kets are combined with tensor=outer product
ccnot operator three input, three output
              the first two kets are the control

test nand, inputs a, b, |1>, outputs ketc
for all 4 cases of a, b, |0> and |1>
nand a=0, b=0
ccnot ketab1 =
vec[0] = (0,0)
vec[1] = (1,0)
vec[2] = (0,0)
vec[3] = (0,0)
vec[4] = (0,0)
vec[5] = (0,0)
vec[6] = (0,0)
vec[7] = (0,0)
ketc=|1>


nand a=0, b=1
ccnot ketab1 =
vec[0] = (0,0)
vec[1] = (0,0)
vec[2] = (0,0)
vec[3] = (1,0)
vec[4] = (0,0)
vec[5] = (0,0)
vec[6] = (0,0)
vec[7] = (0,0)
ketc=|1>


nand a=1, b=0
ccnot ketab1 =
vec[0] = (0,0)
vec[1] = (0,0)
vec[2] = (0,0)
vec[3] = (0,0)
vec[4] = (0,0)
vec[5] = (1,0)
vec[6] = (0,0)
vec[7] = (0,0)
ketc=|1>


nand a=1, b=1
ccnot ketab1 =
vec[0] = (0,0)
vec[1] = (0,0)
vec[2] = (0,0)
vec[3] = (0,0)
vec[4] = (0,0)
vec[5] = (0,0)
vec[6] = (1,0)
vec[7] = (0,0)
ketc=|0>


circuit diagram for quantum nand

  a --.----- a
      |
  b --.----- b
      |
|1> --X------ nand = not(a and b)

truth table output
inputs   | output
a    b   | nand = not(a and b)
---------|------
|0> |0>  | |1>
|0> |1>  | |1>
|1> |0>  | |1>
|1> |1>  | |0>

nand.cpp finished