This is not finished.
2020-07-30 first commit
The problem definition
Traverse field Ising model
Adibatic quantum computation
Trival state preparation
After several days of thinking and researching, I decided to answer my own question.
N.B. The tensor product symbol are omitted when there is no risk in confusion, especially when the index is different. In symbol,
Firstly, for case
we only consider qubit , in which . As and act on different qubits,
For the Ising traverse field Hamiltonian, we only consider
For , it can be evaluated as
We can calculate two-qubit operations independently, such that
Numerically, if you cannot convince yourself,
Now, for a more specific example,