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Use SVD-based fidelity for density matrices and add numerical stability test#7292

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9 changes: 4 additions & 5 deletionscirq-core/cirq/qis/measures.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -242,11 +242,10 @@ def _fidelity_state_vectors_or_density_matrices(state1: np.ndarray, state2: np.n
# state1 is a density matrix and state2 is a state vector
return np.real(np.conjugate(state2) @ state1 @ state2)
elif state1.ndim == 2 and state2.ndim == 2:
# Both density matrices
state1_sqrt = _sqrt_positive_semidefinite_matrix(state1)
eigs = linalg.eigvalsh(state1_sqrt @ state2 @ state1_sqrt)
trace = np.sum(np.sqrt(np.abs(eigs)))
return trace**2
# Both density matrices: use SVD-based fidelity for numerical stability
rho1_sqrt = linalg.sqrtm(state1)
rho2_sqrt = linalg.sqrtm(state2)
return (np.sum(linalg.svdvals(rho1_sqrt @ rho2_sqrt))) ** 2
# matrix is reshaped before this point
raise ValueError( # pragma: no cover
'The given arrays must be one- or two-dimensional. '
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26 changes: 26 additions & 0 deletionscirq-core/cirq/qis/measures_test.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -20,6 +20,8 @@
import pytest

import cirq
import cirq.qis.measures as measures
from cirq import partial_trace

N = 15
VEC1 = cirq.testing.random_superposition(N)
Expand DownExpand Up@@ -187,6 +189,30 @@ def test_fidelity_bad_shape() -> None:
_ = cirq.fidelity(np.array([[[1.0]]]), np.array([[[1.0]]]), qid_shape=(1,))


def test_fidelity_numerical_stability_high_dim():
init_qubits = 10
final_qubits = init_qubits - 1
rng = np.random.RandomState(42)
psi = rng.randn(2**init_qubits) + 1j * rng.randn(2**init_qubits)
psi /= np.linalg.norm(psi)
rho = np.outer(psi, np.conjugate(psi))
rho_reshaped = rho.reshape((2,) * (init_qubits * 2))
keep_idxs = list(range(final_qubits))
rho_reduced = partial_trace(rho_reshaped, keep_idxs).reshape((2**final_qubits,) * 2)

# Direct fidelity computation (old)
rho1_sqrt = measures._sqrt_positive_semidefinite_matrix(rho_reduced)
eigs = measures.linalg.eigvalsh(rho1_sqrt @ rho_reduced @ rho1_sqrt)
cirq_fidelity = (np.sum(np.sqrt(np.abs(eigs)))) ** 2
# SVD-based fidelity (patched)
get_fidelity = cirq.fidelity(
rho_reduced, rho_reduced, validate=False, qid_shape=(2,) * final_qubits
)
# Old version should exceed 1, new should be ~1
assert cirq_fidelity > 1 + 1e-6
assert get_fidelity == pytest.approx(1, abs=1e-6)


def test_von_neumann_entropy() -> None:
# 1x1 matrix
assert cirq.von_neumann_entropy(np.array([[1]])) == 0
Expand Down
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