# Phase estimation of the Pauli-Y matrix

I'm trying to use the phase estimation algorithm to extract the eigen value for both eigen vectors of the Pauli-Y matrix using the ibm quantum experiance.

So far I have this for the possitive state |+>

and this for the negative state |->

However I assumed they would be different but they are currently giving me the same result, is this due to me incorrectly flipping the state from + -> - or is there something else going on here?

• Not confident enough in my fundamentals to post a true answer, but three things look off to me: 1. |+⟩ and |-⟩ aren't the eigenvectors of Y. I think you need to include an extra π/2 Z rotation on q1 to both circuits? 2. Is there some reason to apply X to q0 in your second circuit? :/ 3. What is the swap at the end doing? :/ May 15, 2023 at 16:35
• I am unsure about the swap gate. You carry out Fourier transform on only one qubit, hence no need for the swap. You mixed qubits for phase and eigenvectors. May 15, 2023 at 20:03

## 1 Answer

Some comments:

• Are you working with quatum phase estimation (qpea) or iterative quantum phase estimation (iqpea)?
• If you are working with qpea you need to define more counting qubits, you are trying to find the phase with only one counting qubits, this means you only two possible values for the phase.
• The quantum fourier transform should only be applied to the counting qubits (not the state qubits where you apply $$Y$$). You are applying the swap and QFT wrongly, for 1 qubit the qft is only an $$H$$.
• You should initialize the lower qubit with an eigenstate of $$Y$$, not $$|+\rangle$$ and $$|-\rangle$$.