cirq.generalized_amplitude_damp

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Returns a GeneralizedAmplitudeDampingChannel with probabilities gamma and p.

cirq.generalized_amplitude_damp(
    p: float, gamma: float
) -> cirq.GeneralizedAmplitudeDampingChannel

Used in the notebooks

This channel evolves a density matrix via:

$$ \rho \rightarrow M_0 \rho M_0^\dagger + M_1 \rho M_1^\dagger

  + M_2 \rho M_2^\dagger + M_3 \rho M_3^\dagger

$$

With:

\[ \begin{aligned} M_0 =& \sqrt{p} \begin{bmatrix} 1 & 0 \\ 0 & \sqrt{1 - \gamma} \end{bmatrix} \\ M_1 =& \sqrt{p} \begin{bmatrix} 0 & \sqrt{\gamma} \\ 0 & 0 \end{bmatrix} \\ M_2 =& \sqrt{1-p} \begin{bmatrix} \sqrt{1-\gamma} & 0 \\ 0 & 1 \end{bmatrix} \\ M_3 =& \sqrt{1-p} \begin{bmatrix} 0 & 0 \\ \sqrt{\gamma} & 0 \end{bmatrix} \end{aligned} \]