How to compute the inverse of a unitary B when it's defined only by B|0⟩=XXXX?

Question

I got confused when reading an article about linear combination of unitary method. It shows its process as the following:

I can't figure out how the effect of $B^{dagger}$ is calculated with the limited information of $B$.
Here
is the article mentioned.
Thanks to you all!

DaftWullie · Accepted Answer

The trick is that you don't need to calculate the inverse of $B$. What you really want to evaluate is
$$
(langle 0|otimes I)(B^dagger otimes I)(text{select}(V))(Botimes I).
$$
So, the point is that you only need $langle 0|B^dagger$ which is the Hermitian conjugate of $B|0rangle$, which you know.

How to compute the inverse of a unitary B when it's defined only by B|0⟩=XXXX?

One Answer

Add your own answers!

Ask a Question