Noise Operators
We describe decoherence by representing it with the Lindblad equation. The Lindblad equation is a master equation determining the time evolution of the density matrix. For pure noise terms it is given by \[ \dot{\rho} = \mathcal{L}(\rho) =-i [\hat{H}, \rho] + \sum_{j,k} \Gamma_{j,k} \left( L_{j}\rho L_{k}^{\dagger} - \frac{1}{2} \{ L_k^{\dagger} L_j, \rho \} \right) \] with the rate matrix \(\Gamma_{j,k}\) and the Lindblad operator \(L_{j}\).
Each Lindblad operator is an operator product (in the qubit case, a decoherence operator product - for more information see spins container chapter). LindbladNoiseOperators are built as HashMaps (Dictionaries) of Lindblad operators and values, in order to build the non-coherent part of the Lindblad master equation: \[ \sum_{j,k} \Gamma_{j,k} \left( L_{j} \rho L_{k}^{\dagger} - \frac{1}{2} \{ L_k^{\dagger} L_j, \rho\} \right) \].
The noise operators in struqture are
QubitLindbladNoiseOperatorBosonLindbladNoiseOperatorFermionLindbladNoiseOperatorMixedLindbladNoiseOperator