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For example, if I had a gate rz(0), it holds no value in a circuit. It comes out to a matrix of [[1,0], [0,1]], which seems to be of no value, but I am wondering if there is any purpose of such gate in a circuit.

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Operations like that can be removed without changing the function of the circuit.

They may be in the circuit to achieve some alternative purpose in context, for example to reserve a particular location for a particular purpose.

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Just to add, sometimes a circuit is described in general way and parameters such as rotation angles are evaluated (for example in Qiskit) based on a particular case the circuit is constructed for. So, a calculated rotation angle can be zero which yields for example gate rz(0). As pointed by Craig Gidney and you, such gate is in fact identity operator and it can be removed from the circuit without affecting its function.

In practise these gates are removed during the circuit transpilation. However, it also depends on optimization level you have set. In some cases these gates are left without change.

Finally, it is worth noting that identity gates can be used for measuring relaxation times on a quantum processor (roughly speaking, put for example 10 identity gates in row on a qubit set to state $|1\rangle$ and measure a probability that the qubit stays in the state $|1\rangle$).

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