process_fidelity

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

Return the process fidelity of a noisy quantum channel.

This process fidelity $F_{\text{pro}}$ is given by

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

Parameters

• channel (QuantumChannel) – noisy quantum channel.
• target (Operator or None) – target unitary operator. If None target is the identity operator [Default: None].
• require_cp (bool) – require channel to be completely-positive [Default: True].
• require_tp (bool) – require channel to be trace-preserving [Default: False].
• require_cptp (bool) – (DEPRECATED) require input channels to be CPTP [Default: False].

Returns

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

Return type

float

Raises

• QiskitError – if the channel and target do not have the same dimensions, or have different input and output dimensions.
• QiskitError – if the channel and target or are not completely-positive (with require_cp=True) or not trace-preserving (with require_tp=True).