#ansatzae — Public Fediverse posts

Adrián Pérez-Salinas coordinated a #benasque session on variational #quantum algorithms. Here's the story what I think I learned :)

People now say various things about the state of the field.
It was clear to me from the very beginning that there will be trainability issues and you can verify it because I haven't written a single paper involving brute force training of circuits.

But.

While, I have been avoiding reading papers on VQAs (until I needed to cite variational diagonalization in context of my proposal to use double-bracket flows for diagonalization on quantum computers), now that the field has reached a milestone, here's a few insights I really like and claim will matter down the line:
- statements about #barrenPlateaus are quantitative
- appearance of barren plateaus is implied by presence of #t-design properties https://arxiv.org/abs/2101.02138
- plateaus result from high 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 #quantumCompiling
- 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.