Dear user, my apologies for misunderstanding your original question.

Regarding specific gate operations mentioned- I only modeled return on the quantum states and probabilities present in the provided expression, proper syntax mentioning a CNOT gate would have changed my initial appraisal.

Regarding observables for the given expression, we can compute probability amplitudes via measurements of operators and square norms associated with collapse of respective wave function distributions informing initialization/scanning loads reduction through powered terms add joint statement using:

⟨𝐴⟩=<Φ(0)|A|Φ(0)>, where 𝐴 is a typical operator : A=α||01⟩⟨10|+β||00⟩⟨00|+γ||11⟩⟨11| + δ||10⟩ ⟨01||(Here arrow brackets refer to dot products)

Without further contextual checks however it is very tough to make judgments or give advice relating more wide-scoped scientific problems with confidence assured.