# cirq.AmplitudeDampingChannel¶

class cirq.AmplitudeDampingChannel(gamma)[source]

Dampen qubit amplitudes through dissipation.

This channel models the effect of energy dissipation to the
surrounding environment.
__init__(gamma) → 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. ValueError – is gamma is not a valid probability.

Methods

 controlled_by(*control_qubits) Returns a controlled version of this gate. num_qubits() The number of qubits this gate acts on. on(*qubits) Returns an application of this gate to the given qubits. on_each(*targets) Returns a list of operations apply this gate to each of the targets. validate_args(qubits) Checks if this gate can be applied to the given qubits. wrap_in_linear_combination(coefficient, …)