I am trying to make an intuitive Mathemtaica program to show the principle of quantum walking. The idea of quantum walking is very simple and direct, but when I try to transfer it into Mathemitca codes, I meet several difficulties.
The principle of quantum walk is introduced here http://susan-stepney.blogspot.jp/2014/02/mathjax.html and here http://xxx.tau.ac.il/abs/quant-ph/0303081
There are two operations in one step:
Coin operation (Hadamard coin H)
Step operation (S)
With these two operations, bellow shows the first three steps of a quantum walk
I hope to express this process in an intuitive Mathematica codes.
The result of one step can be expressed as
The two operators, H and S, are put on these two variables
I do not know how to realize such a tensor product in Mathemcatica.
where S and H are two operators; x and y are two variables; x is an array; y is an integer.
But I guess this equation is correct, because similar equation is shown in wiki( http://en.wikipedia.org/wiki/Tensor_product)
To realize this equation in Mathematica, I test an example first, as shown below .
My expected result is
But I cannot obtain this result.
My questions are:
How can I realize in Mathematica？
How to intuitively express the first three steps of quantum walk using Mathematica codes?
I have tried to solve this problem for several days, but made no progress. Any help or suggestion will be highly appreciated,