# cirq.amplitude_damp

Returns an AmplitudeDampingChannel with the given probability gamma.

### Used in the notebooks

Used in the tutorials

This channel evolves a density matrix via:

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

#### With:

\begin{aligned} M_0 =& \begin{bmatrix} 1 & 0 \\ 0 & \sqrt{1 - \gamma} \end{bmatrix} \\ M_1 =& \begin{bmatrix} 0 & \sqrt{\gamma} \\ 0 & 0 \end{bmatrix} \end{aligned}

gamma the probability of the interaction being dissipative.

ValueError if gamma is not a valid probability.

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