Introduction

QuantumGraining.jl offers a practical, generalized approach to the time-coarse graining (TCG) method in quantum optics. Often in quantum optics, we are not interested in the short time-scale dynamics – they are either trivial, or unmeasurable, and keeping track of them is very computationally expensive. The time-coarse graning approach gives an effective description for the time-coarse grained dynamics, while preserving the slow time-scale effects of the short time-scale dynamics.

The main challenge with the TCG approach is that the calculations are very involved, with the number of terms growing rapidly with the order of truncation. QuantumGraining.jl automates this process, representing the effective Lindbladians in terms of abstract operators that are easily integrated into other symbolic packages, such as QuantumCumulants.jl and QuantumOptics.jl.

• The model (Hamiltonian) is specified, along with the time-coarse graining time-scale.
• The effective Lindbladian is calculated, using an efficient, recursive approach. The resulting Lindbladian is stored stored as a symbolic expression using the Symbolics.jl framework, which is also used for any additional simplification and rewriting.
• Finally, the symbolic Hamiltonian can be solved in QuantumOptics.jl or using QuantumCumulants.jl.

Installation

To be added.