Use SVD-based fidelity for density matrices and add numerical stability test #7292
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Summary
Fixes #4819
This PR replaces the existing eigen‑decomposition formula for two density matrices
with an equivalent but more accurate form
This ensures fidelity never exceeds 1 due to round‑off error in higher dimensions.
What’s Changed
In cirq/qis/measures.py, the density‑matrix branch of _fidelity_state_vectors_or_density_matrices now uses sqrtm + svdvals.
A new unit test test_fidelity_numerical_stability_high_dim in measures_test.py constructs a 10‑qubit pure state, traces out one qubit, and verifies that the old eigen‑value‑based fidelity exceeds 1, and the new SVD‑based fidelity ≈ 1.
Testing
Ran pytest cirq-core/cirq/qis/measures_test.py::test_fidelity_numerical_stability_high_dim — old formula fails (>1), new passes (≈1).