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My problem is easy to understand, just how to calculate the matrix of phase operator(or phase gate) acts on multi-qubits so that i can perfrom it in quantum circuit on IBM Quantum Experience

just like the controlled-U gate in phase estimation:

enter image description here

for example:

$$U(y)|φ\rangle=\exp(2πiy)|φ\rangle$$

where $|φ\rangle$ is a two- or three-qubit register.

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  • $\begingroup$ Welcome to QCSE! The way it's currently defined, $U$ is identity up to global phase, so controlled-$U$ is just a single-qubit $Z$ rotation on the control qubit. Is this really the operation you have in mind? $\endgroup$ – Adam Zalcman Feb 14 at 17:44
  • $\begingroup$ @Adam Zalcman thanks a lot for viewing this The operation U in my mind is the one defined in Phase Estimation,I know that normal U gate can change the phase of a single-qubit, and I want to find a way to define 'U' gate that can change the phase of a quantum state contains multi-qubit,such as |000>,|010> and so on. Simply apply U gate on each single-qubit doesn't work cause the phase on single-qubit will also join the tensor product process. I think it's possible to find the matrix of such operator use linear algebra knowledge but so far I haven't find a way $\endgroup$ – leafkoi Feb 15 at 2:24

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