Add the ability to checkpoint configuration recovery

[mcbennet]

Description

These changes introduce the ability to checkpoint configuration recovery and should close #233.

Key Changes:

• Added an initial_state argument to diagonalize_fermionic_hamiltonian to accept a previously saved SCIState.

• Abstracted _extract_carryover_strings to extract high-weight alpha and beta bitstrings from initial_state to seed the next iteration. Important note, I refactored the carryover extraction to use np.nonzero instead of np.argsort and np.searchsorted. This reduces the thresholding step from O(NlogN) to O(N).

• Included a quick fix to docs/guides/integrate_fulqrum.ipynb. The CI was failing because a recent update to fulqrum removed the verbose=False argument from to_csr_linearoperator_fast() (see qiskit-community/fulqrum@60bc326).

Testing

• Testing environment:

  • Python version: 3.13.13
  • Operating system: Fedora Linux

• Added a test that verifies interrupting then resuming via initial_state produces the same mathematical progression as a continuous run.

• Added test for new _extract_carryover_strings helper

• All test/ unittests pass

• Ruff formatting and linting pass