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# qiskit.quantum_info.analysis.distance의 소스 코드

# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2019.
#
# obtain a copy of this license in the LICENSE.txt file in the root directory
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.

"""A collection of discrete probability metrics."""
import numpy as np

[문서]def hellinger_fidelity(dist_p, dist_q):
"""Computes the Hellinger fidelity between
two counts distributions.

The fidelity is defined as 1-H where H is the
Hellinger distance.  This value is bounded
in the range [0, 1].

Parameters:
dist_p (dict): First dict of counts.
dist_q (dict): Second dict of counts.

Returns:
float: Fidelity

Example:

.. jupyter-execute::

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())
"""
p_sum = sum(dist_p.values())
q_sum = sum(dist_q.values())

p_normed = {}
for key, val in dist_p.items():
p_normed[key] = val/p_sum

q_normed = {}
for key, val in dist_q.items():
q_normed[key] = val/q_sum

total = 0
for key, val in p_normed.items():
if key in q_normed.keys():
total += (np.sqrt(val) - np.sqrt(q_normed[key]))**2
del q_normed[key]
else:
total += val
total += sum(q_normed.values())

dist = np.sqrt(total)/np.sqrt(2)

return 1-dist