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

\[F_{\text{pro}}(\mathcal{E}, \mathcal{F}) = F(\rho_{\mathcal{E}}, \rho_{\mathcal{F}})\]

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

\[F_{\text{pro}}(\mathcal{E}, U) = \frac{Tr[S_U^\dagger S_{\mathcal{E}}]}{d^2}\]

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 \(Tr_{\mbox{out}}[\mathcal{E}] - I\) [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.