[10/10] Huge thanks to my collaborators @supanut-thanasilp.bsky.social and @thipchotibut.bsky.social
for being my emotional and academic support throughout this journey. It was a truly amazing experience.

[9/10] Crucially, we observe the separation between saturated BP-appearing quench in MBL and thermalized. This separation keeps growing with the system size !!!

So now I hope you see where you should initialize our training. 😊

[8/10] Our finding that loss variances shrink as the number of quenches makes the ansatz approach a unitary 2-design, irrespective of the quantum phase, is in line with the previous study connecting expressivity and BPs: arxiv.org/abs/2101.02138.

[7/10] We found both phases become maximally expressive in the deep-quench limit, but BPs appear at far fewer quench in the thermalized phase than in the MBL phase.

This is because much larger portion of the Hilbert space is explored during each quench in the thermalized phase.

[6/10] Before we continue, let me sneak in a quick question:

❓How this practical initialization strategy comes from

We need to answer "How quantum phases shape fundamental properties of analog VQAs" first.

[5/10] Yes, we should do the MBL initialization.

[4/10] 🔑 Our key message is that there exists an intermediate regime where quenches are shallow enough to initially avoid BPs in the MBL phase, yet deep enough that the corresponding thermalized phase is maximally expressive.

So, what should we do in this regime?

[3/10] Here, we study a complementary approach which uses native many-body dynamics of analog quantum simulators to build an ansatz.

Our analog system consisting of M quenches can be tuned in-and-out between thermalized and Many-Body Localized (MBL) phases.

[2/10] While the parametrized states in VQAs are typically built through a sequence of digital quantum gates and can achieve universality with deep circuit.

The expressivity can be excessive for a given task and has been identified as a root cause of Barren Plateaus (BPs).