PKB

 Working through Sharma lesson 8, phase kickback... (again). Had

been finding it hard to understand how this is possible. In classical logic, 

an if->then gate means that the second state happens if the first condition is satisfied.

But in quantum computing, under conditions of superposition, the phase of the 

first condition gets altered...

In effect, sharing a phase is necessary for the second qubit to change. We are talking

about a physical system.

Indeed, even under the best conditions, the statevector of the whole needs to add up

to 1.

                                                                     

For phase kickback to be noticeable,  qubit2 has to be in an initial + state.

The sequence of X and H (which yields a negative phase):

                                                                            

                                    

The Phase 'kickback' (the normally positive H on qubit 1 shows up negative):

                                                                   

And each of the four possibilities has a 25% probability.

                                                            *     *     *

Same story with a cntrolled t_gate (which is a Pauli-Z gate set to pi/4).