Fragments are neither Hermitian nor anti-Hermitian

[max-radin]

When generating quantum resource estimates, many of the Hamiltonians (for example fcidump.41_1_ts_noncan_0.2_new.2f0b6ced-7831-4fe0-b95e-ce4d456c9c6b) give warnings about the double-factorized fragments being neither Hermitian nor anti-Hermitian. Based on discussion with @kjm538 this could potentially indicate a problem with the resource estimates. We should investigate this and make changes as needed.

/Users/maxradin/anaconda3/lib/python3.11/site-packages/pyLIQTR/ProblemInstances/ChemicalHamiltonian.py:130: UserWarning: Fragment 654 is neither Hermitian or anti-Hermitian!
  return DF_decomposition(h0, one_body_tensor, two_body_tensor,tol=sf_error_threshold)

[aakunitsa]

Hi @max-radin, did the warning appear for a particular value of the sf_error_threshold? I couldn't reproduce it for id = 41 with the threshold of 1e-4.

[jp7745]

nohup.out.txt

I was running the LRE script and caught the error messages about fragments for a few associated Hamiltonians. See the attached log.

[max-radin]

@aakunitsa I'm seeing the warning with sf_error_threshold set to 1e-12, which is the value currently used by the LRE script. However I don't get the warning when the threshold is set to 1e-4 or 1e-8. So it looks like it is only for certain values of the sf threshold.

qb-gsee-benchmark/src/qb_gsee_benchmark/qre.py

Line 155 in a60a05a

sf_error_threshold=1e-12, # See https://github.com/isi-usc-edu/pyLIQTR/issues/21

[kjm538]

@aakunitsa I'm seeing the warning with sf_error_threshold set to 1e-12, which is the value currently used by the LRE script. However I don't get the warning when the threshold is set to 1e-4 or 1e-8. So it looks like it is only for certain values of the sf threshold.

qb-gsee-benchmark/src/qb_gsee_benchmark/qre.py

Line 155 in a60a05a

sf_error_threshold=1e-12, # See https://github.com/isi-usc-edu/pyLIQTR/issues/21

It sounds like this could be a precision issue. The relevant part of the pyLIQTR code is here:

https://github.com/isi-usc-edu/pyLIQTR/blob/c0760eab7363f6a1fd389cadc7b52b7dea06c1d9/src/pyLIQTR/utils/df_utils.py#L233-L243

where tiny=1e-12 by default. (and the input tol for this function is the sf_error_threshold).

[aakunitsa]

Thank you for investigating @max-radin, @kjm538, and @jp7745! Do we have a sense of whether sf_error_threshold=1e-12 is really necessary? Now that I have the MPSs for all the coarse set instances from Josh, I can try to estimate the thresholds required for chemical accuracy and let you know what I find (especially since Max already made a script for that :))

[max-radin]

Here's a table showing the effect of the sf threshold on LREs for blue_dimer (the problem instance which the Hamiltonian above belongs to). Decreasing the threshold from 1e-8 and 1e-12 increases the T count a bit (26% in the most extreme case). The increase in number of logical qubits however is negligible.

I think the fact that the higher threshold eliminates the warning message but still yields qualitatively similar estimates supports @kjm538's suggestion that this is just some sort of numerical precision issue. I would suggest that we downgrade this issue to low priority.

If/when we want to dig more into this, we could look at how far the fragments are from being (anti-)Hermitian, and also use MPS's to estimate the energy error incurred by sf truncation as @aakunitsa suggested. (I think this would require some modification of our old script though because right now I believe it only considers df truncation.)

Task UUID	T gates (1e-12 threshold)	T gates (1e-8 threshold)	Logical qubits (1e-12 threshold)	Logical qubits (1e-8 threshold)
9da97ef6-4bad-4c82-8576-9b8e539a7ba8	1916519744	1916519744	548	548
f20db1b1-86e3-4ddf-96ff-a6d37f331935	3131753792	3131753792	667	667
742be33c-0982-4b06-b324-1d86242e28d9	40376403840	33274267392	1040	1035
3b49563d-948a-4ecb-84a0-d3c0c2c0d217	46965131136	38051186560	1092	1092
950da653-13ce-4cd7-95d8-5045ab03d4bc	1920451904	1920451904	548	548
13821f5c-78a6-485c-9006-a17a234cde9f	3134768448	3134768448	667	667
765594e5-44ac-41a2-89a7-f2ac03536379	19790006024	16499246736	1039	1034
858b9683-fc6c-4ebe-8c33-27f0d848f24f	46641645440	37106812672	1092	1090
1a013e9f-7eab-4a1b-b486-1d9e2d99e754	2179253568	2171913536	590	590
001a0d11-165a-49c5-a334-643023029f40	11765450264	11047175704	845	845
1c9508e3-b9fe-44f1-ae58-c6339ef43f47	40271021952	33629210368	1040	1038
6713517a-ab65-4381-aae1-0839dcd6c1a0	47367784320	38470092672	1092	1092