Adding Heavy-hex lattice

[PhilipVinc]

I would like to add the heavy hex lattice as a built-in one in netket to make it easy to look at ibm's stuff.

This is relatively easy to do, thanks to @attila-i-szabo implementation of lattice, and I think can be done by adding two new sites to the unit cell

import netket as nk

extent = (2,2)
site_offsets = [
    [0.50, 0.50 / 3**0.5],
    [0.75, 0.75 / 3**0.5],
    [1.00, 1.00 / 3**0.5],
    [1.25, 0.75 / 3**0.5],
    [1.00, 1.50 / 3**0.5],
]

g = nk.graph._common_lattices._hexagonal_general(
    extent=extent,
    site_offsets=site_offsets,
    pbc=False,
)

but this gives the following graph

which is correct, but does not really match the way that IBM does it (also, the 'unit' used by ibm corresponds to 2 unit cells in this representation.

But the way IBM uses this lattice is that... they have a certain number of unit cells plus some extra sites.
I'm unsure how to do it exactly if we want to keep using a Lattice...
Indeed we could just hardcode the same graph structure that they use, but maybe I'm missing something...

[attila-i-szabo]

Do you want the exact structure in Fig.2 here? I suspect that would need additional work because at least the black dots at the very top and very bottom don't match the periodic structure in the bulk

[PhilipVinc]

almost. The shape used by ibm devices is this one, which as you correctly point out is not really a periodic lattice because of the extra sites

[attila-i-szabo]

Yeah. Idk what the best way of constructing this would be - quite possibly just a snaking chain + vertical bonds added by hand

[gcarleo]

do they have a map of the connectivy that can be just downloaded? I think it's much easier to define a custom graph and that's it, then all symmetries should be still doable automatically

[PhilipVinc]

retworkx , IBM's reimplementation of networkx in rust, does generate their interpretation of an heavy-hex graph, but the code is messy. Someone should either ask gpt4 or take a student and make him write it.

[gcarleo]

if that code generates an adjacency list... I think we don't need to implement it in netket, I would just call that code and put the adjacency list in one of our graph-based objects ?

[PhilipVinc]

and erroring if the user has not installed retworkx? indeed that's the simplest option.

[attila-i-szabo]

then all symmetries should be still doable automatically

I think this structure has at most a 180° rotation symmetry, so there's not a whole lot to be gained from the lattice code anyway

[gcarleo]

No I mean I think we shouldn't even support it, it's oo specialized/not a standard lattice I think, if someone wants to use this lattice they can call the IBM library and convert it I to a graph we can use? Maybe we can add an example, not sure