# Why must we take multiple measurements for different values of $M$?

The circuit for Kitaev phase estimation is given as:

By varying $$\theta$$, we are able to determine $$\sin(2 \pi M \phi_k)$$ and $$\cos (2 \pi M \phi_k)$$ from sampling the circuit and calculating the probabilities of different outputs of the first qubit ($$\phi_k$$ is a real number, with $$e^{2 \pi i \phi_k}$$ being the eigenvalue corresponding to $$U$$ and $$|\xi_k\rangle$$). This makes sense, except, the paper I'm reading says we have to take measurements with different values of $$M$$ to get maximum precision for our algorithm's output. Why is this the case?

• Can you link the paper? Oct 23 '19 at 17:04
• @MahathiVempati I'm reading this paper: arxiv.org/pdf/1304.0741.pdf alongside this one arxiv.org/abs/1802.00171. Both use the same process for phase estimation. Oct 23 '19 at 19:39