z iL 0SrSSKJr SSKrSSjrSSjrg)z-A collection of discrete probability metrics.) annotationsNc:[UR55n[UR55n0nUR5H upVXb- XE'M 0nUR5H upVXc- Xu'M SnUR5HGupVXW;a9U[R"U5[R"Xu5- S-- nXu MCX- nMI U[UR55- n[R"U5[R"S5- n U $)a&Computes the Hellinger distance between two counts distributions. Parameters: dist_p (dict): First dict of counts. dist_q (dict): Second dict of counts. Returns: float: Distance References: `Hellinger Distance @ wikipedia `_ r)sumvaluesitemsmathsqrt) dist_pdist_qp_sumq_sump_normedkeyvalq_normedtotaldists _/home/james-whalen/.local/lib/python3.13/site-packages/qiskit/quantum_info/analysis/distance.pyhellinger_distancers   E   EHLLN  #HLLN  # ENN$ ? diintyy'??AE EE LE %  S" ##E 99U diil *D Kc.[X5nSUS-- S-$)aComputes the Hellinger fidelity between two counts distributions. The fidelity is defined as :math:`\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 :math:`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. Parameters: dist_p (dict): First dict of counts. dist_q (dict): Second dict of counts. Returns: float: Fidelity Example: .. plot:: :include-source: :nofigs: from qiskit import QuantumCircuit from qiskit.quantum_info.analysis import hellinger_fidelity from qiskit.providers.basic_provider import BasicSimulator 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 = BasicSimulator() res1 = sim.run(qc).result() res2 = sim.run(qc).result() hellinger_fidelity(res1.get_counts(), res2.get_counts()) References: `Quantum Fidelity @ wikipedia `_ `Hellinger Distance @ wikipedia `_ r)r)r r rs rhellinger_fidelityr9s"\ f -D aKA r)r dictr rreturnfloat)__doc__ __future__rr rrrrr!s4" $N/r