Codebook: Block encoding LCUs

[CatalinaAlbornoz]

Ask here about the “Block encoding LCUs” Codebook topic from the “ Hamiltonian Simulation” module.

[paliyeva]

I have a question about the vector phi (not psi) in one of the bullet points below:

While I understand that the perpendicular state cannot have any 0 components, I am not sure where the <phi| comes from in this context. Is this simply a typo (should be psi instead of phi)? Further, why do we have the bra of the vector not the ket?

Thanks!

[daniela.murcillo]

Hi @paliyeva
Welcome to the forum.
You are right, that was a typo. And I think what having the bra meant was that it was perpendicular regardless of the state being in the subspace M, the full expression being something along the lines of _A\langle 0 | _M\langle \phi | \psi^{\perp}\rangle_{AM} .

We have fixed these lines in the Codebook.

Thanks!