57 lines
1.7 KiB
Plaintext
57 lines
1.7 KiB
Plaintext
---
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title: hellinger_fidelity
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description: API reference for qiskit.quantum_info.hellinger_fidelity
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in_page_toc_min_heading_level: 1
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python_api_type: function
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python_api_name: qiskit.quantum_info.hellinger_fidelity
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---
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# qiskit.quantum\_info.hellinger\_fidelity
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<Function id="qiskit.quantum_info.hellinger_fidelity" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.23/qiskit/quantum_info/analysis/distance.py" signature="hellinger_fidelity(dist_p, dist_q)">
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Computes the Hellinger fidelity between two counts distributions.
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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].
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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.
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**Parameters**
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* **dist\_p** (*dict*) – First dict of counts.
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* **dist\_q** (*dict*) – Second dict of counts.
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**Returns**
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Fidelity
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**Return type**
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float
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**Example**
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```python
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from qiskit import QuantumCircuit, execute, BasicAer
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from qiskit.quantum_info.analysis import hellinger_fidelity
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qc = QuantumCircuit(5, 5)
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qc.h(2)
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qc.cx(2, 1)
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qc.cx(2, 3)
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qc.cx(3, 4)
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qc.cx(1, 0)
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qc.measure(range(5), range(5))
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sim = BasicAer.get_backend('qasm_simulator')
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res1 = execute(qc, sim).result()
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res2 = execute(qc, sim).result()
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hellinger_fidelity(res1.get_counts(), res2.get_counts())
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```
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**References**
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[Quantum Fidelity @ wikipedia](https://en.wikipedia.org/wiki/Fidelity_of_quantum_states) [Hellinger Distance @ wikipedia](https://en.wikipedia.org/wiki/Hellinger_distance)
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</Function>
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