Qiskit / qiskit-addon-sqd / 39512718744

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Fix orbital rotation antisymmetry and in-place k_flat optimization (#410)

Fix two bugs in orbital optimization:

1. _antisymmetric_matrix_from_upper_tri set the lower triangle via
jnp.tril_indices(k_dim, k=-1) with -k_flat, but row-major order of the
lower triangle differs from the transpose of the upper triangle for
dimension 4 or greater. This caused K[j, i] != -K[i, j], so expm(K) was
not orthogonal and rotate_integrals altered the spectrum of the
Hamiltonian. Fixing this by subtracting upper.T from upper guarantees
exact antisymmetry for all dimensions.

2. In _optimize_orbitals_sci, subtracting the JAX gradient array from
k_flat (k_flat -= prev_update) resulted in Python rebinding the local
variable rather than modifying the caller's NumPy array in place. Converting
the JAX gradient with np.asarray ensures in-place subtraction updates the
caller's array.

Adds regression tests verifying that _antisymmetric_matrix_from_upper_tri
generates strictly antisymmetric matrices, that rotate_integrals preserves
the FCI spectrum for norb >= 4, and that optimize_orbitals updates
k_flat in place.

Fixes #390.

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

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