Qubitization demo

[KetpuntoG]

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[KetpuntoG]

[sc-63853]

[gmlejarza]

Very nice demo @KetpuntoG! It explains the basics of qubitization in a very accessible way. I'll write you here some suggestions that we have discussed in person.

Rendering/format suggestions:

1. its eigenvalues encode the eigenvalues of H
2. { $1,e^{\pm i \theta}$ } -> $e^{\pm i \theta}$
3. $\text{PSP}_{\mathcal{H}$

Content suggestions

1. In Qubitization as a rotation: emphasize why we need a rotation (eigenvalue $e^{\pm i \theta}$) and not a reflexion (eigenvalue $\pm 1$)
2. In Qubitization in PennyLane: maybe include the form of the matrix of the Qubitization operator $Q$.
3. In Qubitization in PennyLane: in where k is the number of terms in the Hamiltonian specify that you refer to the number of Pauli matrices in the LCU decomposition. Otherwise it might seem like the number of terms in the Hamiltonian matrix.
4. In Qubitization in PennyLane: maybe including a picture of the circuit for QPE using the $Q$ operator as our $U$ will be clarifying.
5. In Qubitization in PennyLane: in the comment Apply QPE with the walk operator maybe change walk operator for Qubitization operator.