# Lecture 018

// QUESTION: what is unknown 2d plane?

## Quantum Phase Estimation

Although Q.P.E. is about complex unitrary eigenvectors and values. This is not what we study today.

In Grover, we can:

• make $|start\rangle \in \mathbb{R}^N$ (by making $|111\rangle$)

• make mystery quantum operation $U$ (that's a "combo")

$\theta$-estimation algorithm measures angles between $|start\rangle$ and $U^k|start\rangle$ for various $k$, it does not require us to know the 2-d plane. // QUESTION: what?// But we need to be able to measure in a basis containing $|start\rangle$

Given an unknown $|start\rangle$, how to you use it to do measurement against $|start\rangle$ multiple times?

def measureAgainstMysteryStart(U, |Start>)
Make T
H on T
If T then U on |Start>
H on T
Measure T
return |Start>


// TODO

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