cirq.generalized_amplitude_damp

cirq.generalized_amplitude_damp(p: float, gamma: float) → cirq.ops.common_channels.GeneralizedAmplitudeDampingChannel

Returns a GeneralizedAmplitudeDampingChannel with the given

probabilities gamma and p.

This channel evolves a density matrix via:

\rho -> 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:

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}

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.