qiskit.quantum_info.hellinger_fidelity¶
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hellinger_fidelity(dist_p, dist_q)[source]¶ 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.
- Parameters
dist_p (dict) – First dict of counts.
dist_q (dict) – Second dict of counts.
- Returns
Fidelity
- Return type
float
Example
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())
0.9999761034230688
References