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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

state1_sqrt=_sqrt_positive_semidefinite_matrix(state1)eigs=eigvalsh(state1_sqrt @state2 @state1_sqrt)trace=sum(sqrt(abs(eigs)))fidelity=trace**2

with an equivalent but more accurate form

rho1_sqrt=scipy.linalg.sqrtm(rho1)rho2_sqrt=scipy.linalg.sqrtm(rho2)fidelity=np.sum(scipy.linalg.svdvals(rho1_sqrt @rho2_sqrt))**2

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).

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codecovbot commentedApr 22, 2025•
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Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.68%. Comparing base (e9a592d) to head (9a46b19).
⚠️ Report is 249 commits behind head on main.

Additional details and impacted files
@@           Coverage Diff           @@##             main    #7292   +/-   ##=======================================  Coverage   98.68%   98.68%           =======================================  Files        1112     1112             Lines       97599    97616   +17     =======================================+ Hits        96315    96334   +19+ Misses       1284     1282    -2

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@github-actionsgithub-actionsbot added the size: S10< lines changed <50 labelApr 30, 2025
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@RevanthGundala would you be able to take a look at the merge conflicts?

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This pull request has been automatically labeled as stale because 90 days have passed without comments or other activity. If no further activity occurs and thestatus/stale label is not removed by a maintainer within 60 days, this pull request will be closed. If you would like to restore its active status, please leave a comment here; doing so will cause the staleness handler to remove the label.

If you have questions or feedback about this process, we welcome your input. You can open a new issue to let us know (please also reference this issue there, for continuity), or reach out to the project maintainers atquantum-oss-maintainers@google.com.

@github-actionsgithub-actionsbot added status/staleThis has been closed due to inactivity for an extended period of time. and removed status/staleThis has been closed due to inactivity for an extended period of time. labelsAug 20, 2025
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This pull request has been automatically labeled as stale because 90 days have passed without comments or other activity. If no further activity occurs and thestatus/stale label is not removed by a maintainer within 60 days, this pull request will be closed. If you would like to restore its active status, please leave a comment here; doing so will cause the staleness handler to remove the label.

If you have questions or feedback about this process, we welcome your input. You can open a new issue to let us know (please also reference this issue there, for continuity), or reach out to the project maintainers atquantum-oss-maintainers@google.com.

@github-actionsgithub-actionsbot added status/staleThis has been closed due to inactivity for an extended period of time. and removed status/staleThis has been closed due to inactivity for an extended period of time. labelsNov 19, 2025
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@vtomolevtomoleAwaiting requested review from vtomolevtomole is a code owner

@viathorviathorAwaiting requested review from viathorviathor is a code owner automatically assigned from quantumlib/cirq-maintainers

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Fidelity calculation for density matrices improvement

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@RevanthGundala@mhucka
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