# qiskit.quantum_info.hellinger_fidelity

`hellinger_fidelity(dist_p, dist_q)`

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())
```

**References**

Quantum Fidelity @ wikipedia(opens in a new tab) Hellinger Distance @ wikipedia(opens in a new tab)

Was this page helpful?

Report a bug or request content on GitHub.