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I want to measure the depth of a circuit, but I do not know which quantum gates should be used when the circuit is decomposed. For example, $ZZ$ rotation (i.e. $e^{i\theta \sigma_z^i\sigma_z^{i+1}}$) can be decomposed as $\text{CNOT}\,R_z(\theta)\,\text{CNOT}$. So, I think the depth of $ZZ$ rotation is 3. However, if $ZZ$ rotation gate exists, then the depth should be 1.
My question is as follows: Which gate set should be used when I measure the depth of a circuit?
There's no universal convention. Normally there will be some context that suggests a gate set to use (e.g. you plan to run on certain hardware that only supports certain gates, or you plan to use a particular error correcting code where certain gates are transversal).
As the above answer mentioned depending on hardware it varies. It can be verified on Qiskit and cirq as they both support depth view, try comparing there standards.
