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Signed-off-by: Scott Thornton <wsttiger@gmail.com>
The centered exponent schedule applies W^(n - M/2) in place of W^n; the extra W^(-M/2) is a phase on each walk eigencomponent, so the exact phase-register marginals of the centered shell and of PhaseEstimation's textbook ladder agree bin by bin (total variation 7e-16 at m=6), not only after mirror folding. Compare the unfolded marginals in the example and the corresponding sampled histograms, drop the local folding helper, and describe the check that way on the examples page and in the guide. Also replace the "must not fold before the sampling check" wording with the reason (folding coarsens a distribution and can only lower total variation), and remove history wording from the docs. Signed-off-by: Scott Thornton <wsttiger@gmail.com>
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Extends the existing H2 QPE tutorial with
PhaseEstimationusing the same Hamiltonian and Hartree–Fock input. The original exact-evolution, Trotter, and centered-walk calculations remain intact. The new section executes measured circuit generation, sampling, and public count decoding, checks textbook versus centered exact folded marginals, and compares seeded unfolded sample distributions to an a priori statistical bound. Energy acceptance uses nonlinear cosine phase cells, with core energy included once.Validation on CUDA-Q 0.16.0.post1, Python 3.12.3, qpp-cpu:
python3 -m pytest tests/python/test_examples.py -k 08_quantum_phase_estimation -q: 1 passed in 57.42 s.-W --keep-going: passed independently.Independent plan 06 PR against main; no sibling example, library change, or new dependency is required.