Adding dbi strategies

[marekgluza]

Update: Matteo prepared this https://github.com/qiboteam/boostvqe/blob/results/extras/load_vqe.py

Please use that on the results branch.

The notebook below can be useful for intuition.

Please show how to modify load_vqe.py so that it uses the group commutators.

Old: Please use notebooks/load_vqe_circuit_apply_GC_rotation.ipynb to add showcasing of gradient descent for 1 local for

• [x] 1 GCI step
• [ ] 2 GCI steps
• [ ] 3 steps

Check the #33 results from Matteo and

• [ ] for each load vqe
• [ ] add GCIs and show which one is best performing

We are searching for the biggest possible decrease of the energy (the fluctuation we don't care)

We would like to be as close as possible to the ground state energy and demonstrate that we lower the energy easily.

The plan ahead is:

• [x] take VQE on a couple of layers, very narrow. Lower the energy to almost what gives a training plateux for many layers
• [x] run GCI for very short depth but try to drop towards the ground state
• [x] we will then compile the XXZ GCI into CNOTs and single qubit rotations see #34
• [x] the boosting paper will then say: we compile circuits beyond vqe capabilities and find ground state approximations (... your results) with (....your results) number of CNOT gates

This will be updated and explained more, but please already

• [x] start exploring the notebook how to load data
• [x] merge Matteo's branch from #33 and load that data too
• [x] focus on the 1 -local model and try to show us if the training works
• [ ] if any troubles please directly ping on Slack

[marekgluza]

the notebook as is shows that one GC step by hand lowers the energy on 8q after 1 VQE layer by 0.5 out of about 10 which is pretty good anyway but let's try to get better. Especially, we want to have the splitting:

• short vqe + DBI
• long vqe both with the same eventual circuit depth. For this to work we need to figure out the tradeoff, when is VQE using its depth meaningfully? Let's say in total 20l then maybe 3l for vqe and 17l for DBI? (Just guessing some numbers) and then we can compare 3+17 vs 20. If we get better than those trainings then we can claim good compiling schemes :)

[marekgluza]

Adding notation for the simulations:

• We start with $H_0$
• we train vqe to get $U_\theta$
• then we rotate $J0 = U\theta^\dagger H0 U\theta$
• we run a DBI step starting from $J_0$ and obtain $J_1 = V^\dagger J_0 V$

What is the state? In the lab we will prepare $$|\psi\rangle = V U_\theta |0\rangle$$

Why does it work? Because $$\langle \psi | H_0 \rangle \psi = \langle 0| J_1|0 \rangle$$