52 lines
2.4 KiB
Plaintext
52 lines
2.4 KiB
Plaintext
---
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title: process_fidelity
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description: API reference for qiskit.quantum_info.process_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.process_fidelity
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---
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# qiskit.quantum\_info.process\_fidelity
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<Function id="qiskit.quantum_info.process_fidelity" isDedicatedPage={true} github="https://github.com/qiskit/qiskit/tree/stable/0.19/qiskit/quantum_info/operators/measures.py" signature="process_fidelity(channel, target=None, require_cp=True, require_tp=True)">
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Return the process fidelity of a noisy quantum channel.
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The process fidelity $F_{\text{pro}}(\mathcal{E}, \mathcal{F})$ between two quantum channels $\mathcal{E}, \mathcal{F}$ is given by
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$$
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F_{\text{pro}}(\mathcal{E}, \mathcal{F})
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= F(\rho_{\mathcal{E}}, \rho_{\mathcal{F}})
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$$
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where $F$ is the [`state_fidelity()`](qiskit.quantum_info.state_fidelity "qiskit.quantum_info.state_fidelity"), $\rho_{\mathcal{E}} = \Lambda_{\mathcal{E}} / d$ is the normalized [`Choi`](qiskit.quantum_info.Choi "qiskit.quantum_info.Choi") matrix for the channel $\mathcal{E}$, and $d$ is the input dimension of $\mathcal{E}$.
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When the target channel is unitary this is equivalent to
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$$
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F_{\text{pro}}(\mathcal{E}, U)
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= \frac{Tr[S_U^\dagger S_{\mathcal{E}}]}{d^2}
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$$
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where $S_{\mathcal{E}}, S_{U}$ are the [`SuperOp`](qiskit.quantum_info.SuperOp "qiskit.quantum_info.SuperOp") matrices for the *input* quantum channel $\mathcal{E}$ and *target* unitary $U$ respectively, and $d$ is the input dimension of the channel.
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**Parameters**
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* **channel** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator") *or QuantumChannel*) – input quantum channel.
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* **target** ([*Operator*](qiskit.quantum_info.Operator "qiskit.quantum_info.Operator") *or QuantumChannel or None*) – target quantum channel. If None target is the identity operator \[Default: None].
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* **require\_cp** (*bool*) – check if input and target channels are completely-positive and if non-CP log warning containing negative eigenvalues of Choi-matrix \[Default: True].
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* **require\_tp** (*bool*) – check if input and target channels are trace-preserving and if non-TP log warning containing negative eigenvalues of partial Choi-matrix $Tr_{\mbox{out}}[\mathcal{E}] - I$ \[Default: True].
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**Returns**
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The process fidelity $F_{\text{pro}}$.
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**Return type**
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float
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**Raises**
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**QiskitError** – if the channel and target do not have the same dimensions.
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</Function>
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