# Generalized Parameter Shift CNOT

Hi, I was wondering how parameter shift rule can be applied to the CNOT gate? I have watched the derivations on the PennyLane Youtube channel but I am slightly confused about where it applies and if it applies to all entangling gates?

The parameter shift rule applies to parameterized gates (with some assumptions made to those gates). The CNOT gate has no parameters — it flips a target qubit if the control qubit is 1 .

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Thank you for clarifying!

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My pleasure! To add to my previous comment, the parameter-shift rule is a differentiation method. The method by which we differentiate aside, let’s just say I have a function f(x). If f(x) is a constant function (e.g., f(x) = 3), then its derivative is zero. However, if f(x) actually depends on x (e.g., f(x) = x^2), then its derivative is non-zero — it’s another function.

The same goes for differentiating gates in a quantum circuit. If a gate doesn’t depend on any variables (like X, Y, Z, Hadamard, CNOT, etc.), then differentiating it with respect to any parameter is a null result and doesn’t need to be accounted for in any way .

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