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I'm reading the Qiskit tutorial on quantum phase estimation. In this tutorial, the controlled unitaries on the diagram are denoted as $U^{2^{t-1}}, ..., U^{2^{0}}$:

enter image description here

In the actual quantum circuit, however, those gates are implemented using controlled phase gates. When I tried to apply QPE to a single-qubit Hamiltonian I'm interested in, it turned out that I need to run 2 histograms separately in order to determine both energies, as in each of the histograms, there will be another eigenvalue associated with the phase gate, which is 1. For example:

enter image description here

In this case, the string '00101' is one of my targets, but '00000' comes from the phase gate.

Now I wonder if it's okay to replace those controlled phase gates with controlled $U_3$ gates to see both energies in one histogram. If I do that, how can I make sure the phase works as we expected? Should I tune the length of time evolution as depicted on the diagram? Thanks!

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  • $\begingroup$ Can you provide your code along with the Unitary gate you're interested in? $\endgroup$
    – Tristan Nemoz
    Feb 4, 2022 at 16:32

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