Thanks to all my collaborators Hela Mhiri, Sacha Lerch, @quantummanuel.bsky.social, @thipchotibut.bsky.social, Supanut Thanasilp, @qzoeholmes.bsky.social

We also reproduce results for previously studied circuits, particularly around the identity, for HVA, HEA, and tensor product ansatz. We use these results to analyze the effect of global/local observables and the impact of correlating parameters.

We use this bound to study different circuits and points on the landscape. In particular, we present a corollary that characterizes the size of the region around the minima. We also focus on studying the region around zero for time-correlated circuits, such as the correlated UCC or HVA circuits.

We analytically prove a generic lower bound on the variance of a loss function. It can be applied around any point on the landscape and for a wide range of circuits. Around any point with substantial curvature, we can prove that there exists a substantial region with (non-exp small) gradients.

New paper on arXiv 🔥
We present a bound that unifies all the previous guarantees of small regions with substantial gradients in BP landscapes. This allows us to study new architectures, parameter correlations, and points on the landscape that could not be analyzed before.
scirate.com/arxiv/2502.0...

However this does not mean that it is not possible to train. To do so the ‘only thing’ we require is a path with substantial gradients. These fertile valleys between barren regions can theoretically exist, but to what extent is unknown. We provide a toy example of this.

A final limitation of our analysis is that the adiabatic minimum need not be the global minimum of the loss. It is possible for the best minimum to jump from the initialization region to another. We show an example in which this seems to happen.

Focusing on an iterative variational method for quantum dynamics as an ideal playground for studying warm starts, we can analytically guarantee substantial gradients and approximate convexity around the initializations at each (small) time-step.

Is a barren plateau landscape trainable? If we start close to the actual solution, then probably yes!?

Here we study variational quantum simulation to explore whether warm starts can be a possible solution to exponential concentration

Our paper titled Variational Quantum Simulation: A Case Study for Understanding Warm Starts has been published in PRX Quantum 🚀

Short explanation 🧵 or you can find the whole paper here: journals.aps.org/prxquantum/a...

Starting from a product state, we present bounds for the Quantum Fisher Information and find physically relevant interactions that approach such bounds.

We study this for the dynamical regime and for the Gibbs and time-averaged dephased state.

New paper on arXiv🔥

How can many-body interactions boost quantum sensing to its limits?

We show how to add controlled interactions in many-body probes to reach the highest precision limits in quantum metrology -- both for dynamical and steady states.

scirate.com/arxiv/2412.0...

#quantum