# cirq.GeneralizedAmplitudeDampingChannel¶

class cirq.GeneralizedAmplitudeDampingChannel(p: float, gamma: float)[source]

Dampen qubit amplitudes through non ideal dissipation.

This channel models the effect of energy dissipation into the environment
as well as the environment depositing energy into the system.
__init__(p: float, gamma: float) → None[source]

The generalized amplitude damping channel.

Construct a channel to model energy dissipation into the environment as
well as the environment depositing energy into the system. The
probabilities with which the energy exchange occur are given by
gamma, and the probability of the environment being not excited is
given by p.
The stationary state of this channel is the diagonal density matrix with
probability p of being |0⟩ and probability 1-p of being |1⟩.

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

Parameters
• gamma – the probability of the interaction being dissipative.

• p – the probability of the qubit and environment exchanging energy.

Raises

ValueError – if gamma or p is not a valid probability.