# cirq.AmplitudeDampingChannel¶

class cirq.AmplitudeDampingChannel(gamma: float)[source]

Dampen qubit amplitudes through dissipation.

This channel models the effect of energy dissipation to the
surrounding environment.
__init__(gamma: float) → None[source]

The amplitude damping channel.

Construct a channel that dissipates energy. The probability of energy
exchange occurring is given by gamma.

This channel evolves a density matrix as follows:

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

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

Parameters

gamma – the probability of the interaction being dissipative.

Raises

ValueError – is gamma is not a valid probability.