I am struggling to understand the concept of updating angles in a parameterized algorithm.
Assume I have an objective function $x^2+1$ that I want to optimize using QAOA which can handle continuous problems. After running one layer of the circuit and measuring, I use a classical minimizer to update the angles/parameters. What is the function that I should give to the minimizer (e.g. COBYLA)? In the textbooks I find the function to optimize is the expectation value, $⟨ψ(γ,β)∣H_C∣ψ(γ,β)⟩$. But isn't the expectation value a scalar? If the function that should be given to the minimiser is the objective function, then how the angles are incorporated?



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