cirq.generalized_amplitude_damp

cirq.generalized_amplitude_damp(p: float, gamma: float) → cirq.ops.common_channels.GeneralizedAmplitudeDampingChannel[source]
Returns a GeneralizedAmplitudeDampingChannel with the given
probabilities gamma and p.

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 – gamma or p is not a valid probability.