Hi @somearthling,

Thanks for the question!

\nabla_\theta U(\theta)= -irGU(\theta)

Could you further describe your line of thinking here?

In specific:

- How come r appears on the right-hand side as a term?

Equation (5) from the paper describes the derivative of a gate generated by a Hermitian operator G:

\partial_\mu \mathcal{G} = -iGe^{-i\mu G}

Using the definition of \mathcal{G}(\mu)=e^{-i\mu G} on the right hand side, equation (5) is equal to:

\partial_\mu \mathcal{G} = -iG\mathcal{G}(\mu)

- If the equation for the gradient of the unitary that you propose does hold, what circuit would we run on real quantum hardware to get the gradient of the variational circuit? I.e., how can you substitute the proposed gradient of the gate into equation (3) of the paper such it’s something we can compute the gradient on real quantum hardware? If you could re-express the gradient of the variational circuit (\partial _\mu f instead of the gradient of a single gate), that would help with the understanding.

Also, assume that the quantum hardware can run the circuit of f, but there should be no further assumptions on additionally supported gates.