Qiskit / qiskit-addon-sqd / 41713581518
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Use Fulqrum's sci_solver factory in the integration guide (backport #427) (#434)

* Use Fulqrum's sci_solver factory in the integration guide (#427)

Fulqrum PR #140 proposes addon_sqd_support, a module that builds an
sci_solver for diagonalize_fermionic_hamiltonian.  If it lands, the guide no
longer has to construct one inline: each of its two solvers collapses to a
single sci_solver_from_integrals call, and the PRIMME section becomes one
eigensolver argument rather than a second copy of the whole solver.

The code this removes is the easiest to get wrong.  Fulqrum orders a
subspace with the beta half string major, so the eigenvector needed
transposing, and fq.Subspace sorts each list of half strings, so the
unpacking depended on the CI strings arriving sorted.  Getting either wrong
leaves the energy correct while attaching amplitudes to the wrong
determinants.

Verified against the old inline solver at the guide's own problem size, same
seed: identical energy (-109.034026675594), identical amplitude shape
(808, 808), and zero difference in amplitudes and occupancies.

Raise the fulqrum extra's floor to 0.5.0, the version that would carry the
module.  That release does not exist yet.

Assisted-by: Claude Opus 5
(cherry picked from commit 36fb70c77)

* Skip the Fulqrum guide in the minimum-version job

The backported guide uses fulqrum.addon_sqd_support, which fulqrum added
in 0.5.0. The minimum-version job pins every dependency to the floor this
branch declares, so it installs 0.4.4 and the notebook fails on import.

Raising the fulqrum floor would fix CI but is the wrong trade on a stable
branch: it would break environments that already satisfy the declared
0.4.4 bound. Skip the notebook in that one job instead. The latest- and
development-version workflows install the current fulqrum and keep
executing it, so the guide stays covered.

tox.ini already passes {posargs} to pytest ahead of docs/, so the ignore
goes in as ... (continued)

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