qiskit.quantum_info.process_fidelity

process_fidelity(channel, target=None, require_cp=True, require_tp=True)

Return the process fidelity of a noisy quantum channel.

The process fidelity $F_{\text{pro}}(\mathcal{E}, \mathcal{F})$ between two quantum channels $\mathcal{E}, \mathcal{F}$ is given by

where $F$ is the state_fidelity(), $\rho_{\mathcal{E}} = \Lambda_{\mathcal{E}} / d$ is the normalized Choi matrix for the channel $\mathcal{E}$, and $d$ is the input dimension of $\mathcal{E}$.

When the target channel is unitary this is equivalent to

where $S_{\mathcal{E}}, S_{U}$ are the SuperOp matrices for the input quantum channel $\mathcal{E}$ and target unitary $U$ respectively, and $d$ is the input dimension of the channel.

Parameters

• channel (Operator or QuantumChannel) – input quantum channel.
• target (Operator or QuantumChannel or None) – target quantum channel. If None target is the identity operator [Default: None].
• 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].
• 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 $Tr_{\text{out}}[\mathcal{E}] - I$ [Default: True].

Returns

The process fidelity $F_{\text{pro}}$.

Return type

float

Raises

QiskitError – if the channel and target do not have the same dimensions.