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The PauliZGate adds a method of instantiating diagonal unitaries. The PauliGate class is ill-suited for this problem because it is over-parameterized; it allows for non-zero non-Z Pauli string elements. There is also a straight forward way of converting these PauliZGates into CNOT+RZ gates [1][2].
[1] https://arxiv.org/abs/2109.03371
[2] https://arxiv.org/abs/1306.3991