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# qiskit.quantum_info.hellinger_fidelity¶

hellinger_fidelity(dist_p, dist_q)[fuente]

Computes the Hellinger fidelity between two counts distributions.

The fidelity is defined as $$\left(1-H^{2}\right)^{2}$$ where H is the Hellinger distance. This value is bounded in the range [0, 1].

This is equivalent to the standard classical fidelity $$F(Q,P)=\left(\sum_{i}\sqrt{p_{i}q_{i}}\right)^{2}$$ that in turn is equal to the quantum state fidelity for diagonal density matrices.

Parámetros
• dist_p (dict) – First dict of counts.

• dist_q (dict) – Second dict of counts.

Devuelve

Fidelity

Tipo del valor devuelto

float

Ejemplo

from qiskit import QuantumCircuit, execute, BasicAer
from qiskit.quantum_info.analysis import hellinger_fidelity

qc = QuantumCircuit(5, 5)
qc.h(2)
qc.cx(2, 1)
qc.cx(2, 3)
qc.cx(3, 4)
qc.cx(1, 0)
qc.measure(range(5), range(5))

sim = BasicAer.get_backend('qasm_simulator')
res1 = execute(qc, sim).result()
res2 = execute(qc, sim).result()

hellinger_fidelity(res1.get_counts(), res2.get_counts())


Referencias