Adrián Pérez-Salinas coordinated a #benasque session on variational #quantum algorithms.

People say various things about the state of the field, here's what I say:
From the beginning it was clear that there will be trainability issues, you can verify that it has been clear to me because I haven't written a single paper involving brute force training of circuits.

But.

While, on purpose, I haven't read a single paper on VQAs (until I needed to cite variational diagonalization to compare to my own proposal for diagonalization on quantum computers) and now that the field has reached a milestone, without having been involved, here's a few things I really like.

I claim it will matter down the line that:
- statements about barren plateaus are quantitative
- appearance of barren plateaus is implied by t-designs properties https://arxiv.org/abs/2101.02138
- plateaus are a result of dimensionality of the training parameter set.

To paraphrase grandmaster Bronstein, it's not about what but how.
We now know very, very well how VQAs go wrong. Early on it was only clear what the problem will be.

Each of the points above can guide better #ansatzae:
- they need to operate on clumped circuits to reduce the dimensionality
- they shouldn't rotate back and forth but use physics equations to guide the quantum compiling
- a restricted ansatz with justified expressibility can be quantitatively tested using the average+variance criteria of regular barren plateaus.

What the field achieved is to inform a large group of people how to recognize what a good variational Ansatz will be once we will encounter it. And that it will not be naive? Come on, easy would have been boring.