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
For examples showing how to use QubitLindbladNoiseOperators, please see the the spins section.
For examples showing how to use FermionLindbladNoiseOperators, please see the the fermions section.
For examples showing how to use BosonLindbladNoiseOperators, please see the the bosons section.
For examples showing how to use MixedLindbladNoiseOperators, please see the the mixed system section.