Improve fidelity of MPS truncation (bond max to bond 2)

[ACE07-Sev]

Greetings there,

Hope all are well. Quick question, I was wondering what is the best way to truncate the bond dimension of an MPS to 2 to maximize fidelity? If the improvement is considerable, I am okay with longer runtime if it requires intensive computation.

[jcmgray]

Hi @ACE07-Sev, the best method for this will be the fitting method, you can up the number of sweeps and it should converge on the best fidelity approximation for the given bond dimension.

[ACE07-Sev]

I out of curiosity did it with one layer (which from what you can see would be about the same normalization and supposedly should yield the same fidelity as one layer with .compress(form="right", max_bond=2)) and it's still near 0. Could it be the permute_arrays=True by default of fitting? I tried setting it off but it gave non-unitary layers.

[ACE07-Sev]

Yeah it's permute arrays. I explicitly set it to lpr now instead of True and the fidelity now matches what .compress(form="right", max_bond=2) does.

Is there a way for it to not mess with permute arrays and just do the same as .compress()? Because explicitly defining it seems like a recipe for logical errors like this for cases where I don't permute my MPS to lpr before calling this method.

[ACE07-Sev]

So, it works really great for volume-law case (without it I get 0.5 maybe, with it 0.99, insane), and tiny improvement over area-law one. Just need to get two things solved:

• Not have it permute arrays, just like .compress() so that I wouldn't have to explicitly hardcode lpr to it.
• Make it more stable. Majority of times for the case I mentioned I get 0.95 - 0.99, but then sometimes it dips to 0.34 or 0.5. I have 1000 iterations so I'm wondering how I can semi-guarantee that performance consistently.

[ACE07-Sev]

I was wondering if you have had a chance to view my last message sir. Much appreciated.

[ACE07-Sev]

So, I ran the encoding on the very same input, and with the variational fitting, I get the following fidelities if I re-run. Just to clarify, this is the exact same cell being run 10 times and that complex number is the fidelity achieved:

Run 1
(0.4996733122490927+2.631727913111198e-08j)
Run 2
(0.7068963576513837+3.0285344092305985e-09j)
Run 3
(0.9999424813962471+3.550997472955529e-10j)
Run 4
(0.7070377317205315+4.3042156971458996e-08j)
Run 5
(0.7070106424566729+3.2127947555696734e-08j)
Run 6
(0.9975961469265427-2.374211866942367e-10j)
Run 7
(0.7069904392205517-3.0109985225406526e-09j)
Run 8
(0.6957782658157091-4.410586209856204e-09j)
Run 9
(0.7897053410811823-1.613496600379443e-08j)
Run 10
(0.9998551150720156+1.2629428468194197e-11j)

Given it can indeed reach 0.99, I'd like to make it more consistent so that it would return that every time.