# qiskit.quantum_info.process_fidelity¶

process_fidelity(channel, target=None, require_cp=True, require_tp=True)[Quellcode]

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.

Parameter
• 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].

Rückgabe

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

Rückgabetyp

float

Verursacht

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