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qiskit.quantum_info.process_fidelity

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

Return the process fidelity of a noisy quantum channel.

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

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

where \(S_{\mathcal{E}}, S_{U}\) are the SuperOp matrices for the input quantum channel \(\cal{E}\) 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).

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