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?

Hadamard Test

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

// TODO