Variational and TDVP kernels

qslib-quantum-variational accepts the numerical products of a wavefunction frontend without depending on an autodiff framework. A caller supplies one complex local energy and one complex log derivative per sample and parameter, in row-major sample order. Non-negative normalized or unnormalized sample weights are accepted; the estimator normalizes them internally.

For real parameters, the estimator forms

S_kl = Re E[conj(delta O_k) delta O_l]
F_k  = E[conj(delta O_k) delta E_loc]

and uses Im(F) for real time or -Re(F) for imaginary time. Energy mean and variance are retained alongside the dense real QGT. DenseQgt::matvec and solve_cg cover dense and caller-supplied matrix-free solves. qgt_vector_product_stream consumes derivative chunks directly, so a frontend can stream rows without constructing a sample-space identity.

Regularization::FixedTikhonov adds a documented diagonal shift, Regularization::Gcv selects a positive shift from a supplied grid, and Regularization::SpectralCutoff removes modes below a relative eigenvalue threshold. Solve results report clipping, QGT metric norm, projected residual, and normalized residual. ParameterLayout records deterministic names, shapes, offsets, and a stable fingerprint for checkpoint compatibility.

The Rust layer does not compute neural-network derivatives. Python and other frontends may adapt their own derivative engines to these checked arrays at a coarse boundary.

For local energy, local_energy_from_ratios expects row-oriented matrix elements (H_{b b'}, psi(b')/psi(b)), including the diagonal separately. A Hamiltonian::apply is column-oriented and returns c * P_ba; do not conjugate that whole coefficient for complex c. Prefer a row/local-energy API, or conjugate only the Pauli matrix element when constructing the pair.