Qiskit / qiskit-addon-sqd / 41739079182
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Restore the stored outputs in the Fulqrum and SBD guides (#435) (#439)

docs/guides/integrate_fulqrum.ipynb lost the stored output of three cells in
#427, which edited the notebook by hand rather than re-executing it.
docs/guides/integrate_sbd.ipynb has never carried output, since #367 added it.
The docs build sets nbsphinx_execute = "never", so the hosted page renders
whatever is stored: both guides published cells with empty output areas.

Re-execute both against released versions (fulqrum 0.5.0, sbd-eigensolver
1.7.2) and store the result.  Every guide notebook now carries output again.

The Fulqrum numbers reproduce what #427 removed to within last-digit float
noise, and its scipy estimate matches the -109.034026675594 that commit's
message recorded, so the refactor it performed was sound; only the outputs
were lost.

SBD's compiled core prints Davidson progress and per-call timings straight to
stdout, and neither solve_sci_batch nor the TPB_SBD config object exposes a
way to quiet it: executing the notebook produces of order 50 kB of solver
chatter across ~250 output blocks.  Storing that verbatim would bury the
guide's point and churn on every re-execution.  Keep PySCF's own messages and
each batch solve's converged energy, and drop the per-iteration traces and the
timings.  The stored output is therefore a trimmed copy of a real run, not
everything the cell prints.

Assisted-by: Claude Opus 5
(cherry picked from commit 2a3718c39)

Co-authored-by: Jim Garrison <garrison@ibm.com>

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