Qiskit / qiskit-addon-sqd / 37474451770

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Add trim SQD (#369)

* Add trim SQD

Trim SQD screens more configurations than it diagonalizes. Where standard
SQD diagonalizes each subsampled batch independently and keeps the best
result, trim SQD treats the batches as candidates: each is diagonalized
and trimmed down to the CI strings carrying the largest weight, and the
survivors of all the batches are merged and diagonalized together. The
merged diagonalization is what the iteration reports, and its own trimmed
strings seed the next configuration recovery iteration.

Screening is cheaper than diagonalizing well. Each batch is roughly the
size of the merged subspace, so a candidate pool several times larger than
the affordable subspace can be ranked for the cost of a few extra
diagonalizations of that size. An iteration costs num_batches + 1
diagonalizations rather than num_batches.

The technique comes from joint research by the Cleveland Clinic
Foundation, RIKEN, and IBM, arXiv:2605.01138. Note that the paper's
workflow also extends the surviving subspace by adding excitations before
a final diagonalization; that step is not implemented here.

Trim SQD is selected through a new `policy` argument of
diagonalize_fermionic_hamiltonian:

    result = diagonalize_fermionic_hamiltonian(
        hcore, eri, bit_array,
        samples_per_batch=300, norb=norb, nelec=nelec, num_batches=5,
        policy=TrimPolicy(trim_ratio=0.1),
        sci_solver=my_distributed_solver,
    )

A policy selects the schedule an iteration follows: how sampled
configurations become subspaces, whether one round of diagonalizations
leads to another, which result the iteration reports, and which CI strings
seed the next one. It is described by the SubspacePolicy protocol;
it returns the subspaces and the loop calls sci_solver with
them, so the schedule and the eigensolver are chosen independently and any
combination works. `policy` defaults to StandardPolicy, the behavior this
function has always had, so omitting it changes ... (continued)

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