Cbits  continued

Lecture 1 1/23/2014

In the previous lecture we have seen how cbits can be written in different ways and how to combine  two or more
cbits to store integers, e.g. a 3-cbit can store the following

({{|000⟩, |001⟩, |010⟩, |011⟩}, {|0⟩, |1 ⟩, |2 ⟩, |3 ⟩}, {(Subscript[|0 ⟩, 3]), (Subscript[|1⟩, 3]), (Subscript[|2 ⟩, 3]), (Subscript[|3⟩, 3])}})

The ket  form (Subscript[| x ⟩, n]) = |a b ... c ⟩ is defined as follows 

(Subscript[|x ⟩, n]) = | (Subscript[y, n-1 ])⟩  ⊗ | (Subscript[y, n-2 ])⟩ ⊗ . . . | (Subscript[y, 1 ])⟩ ⊗ | (Subscript[y, 0 ])⟩ 

where the quantity x and the coefficients are related via

x  = (Underoverscript[ ∑  , (j=0), (n-1)])(Subscript[y, j ])(2^j)

We also have the matrix representation

| 0 > =(({{1}, {0}}))

| 1 > =(({{0}, {1}}))

Using Mathematica to construct and manipulate cbits

zero={1,0};
MatrixForm[zero]
one={0,1};
MatrixForm[one]

product=Flatten[KroneckerProduct[zero,zero,zero]];
MatrixForm[product]