g" .dZddlmZddlZd d Zd d ZdS) z-A collection of discrete probability metrics.) annotationsNdist_pdictdist_qreturnfloatcpt|}t|}i}|D] \}}||z ||<i}|D] \}}||z ||<d}|D]G\}}||vr9|tj|tj||z dzz }||=B||z }H|t|z }tj|tjdz } | S)aJComputes 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) rrp_sumq_sump_normedkeyvalq_normedtotaldists [/granary/edev/quantum/lib/python3.11/site-packages/qiskit/quantum_info/analysis/distance.pyhellinger_distancers2   E   EHLLNN$$Se  HLLNN$$Se  ENN$$S (?? dinnty#'?'??AE EE SLEE S"" # ##E 9U  dill *D Kc8t||}d|dzz dzS)avComputes the Hellinger fidelity between two counts distributions. The fidelity is defined as :math:`\left(1-H^{2}\right)^{2}` where H is the Hellinger distance. This value is bounded in the range [0, 1]. This is equivalent to the standard classical fidelity :math:`F(Q,P)=\left(\sum_{i}\sqrt{p_{i}q_{i}}\right)^{2}` that in turn is equal to the quantum state fidelity for diagonal density matrices. Parameters: dist_p (dict): First dict of counts. dist_q (dict): Second dict of counts. Returns: float: Fidelity Example: .. code-block:: from qiskit import QuantumCircuit from qiskit.quantum_info.analysis import hellinger_fidelity from qiskit.providers.basic_provider import BasicSimulator qc = QuantumCircuit(5, 5) qc.h(2) qc.cx(2, 1) qc.cx(2, 3) qc.cx(3, 4) qc.cx(1, 0) qc.measure(range(5), range(5)) sim = BasicSimulator() res1 = sim.run(qc).result() res2 = sim.run(qc).result() hellinger_fidelity(res1.get_counts(), res2.get_counts()) References: `Quantum Fidelity @ wikipedia `_ `Hellinger Distance @ wikipedia `_ r )r)rrrs rhellinger_fidelityr9s'X ff - -D aKA r)rrrrrr)__doc__ __future__rrrrrrr!s[43"""""" $$$$N------r