SLHQuantumSystems.jl

SLHQuantumSystems.jl is a Julia package for creating and composing open quantum systems using the SLH framework.

Quick Start

Get started by running one of the examples!

julia> include("examples/cascadedcavities.jl")SLH("sys", SLHQuantumSystems.Subspace[OpticalMode("A_A"), OpticalMode("B_B")], Dict{Symbol, Symbolics.Num}(:A_A_l => A_A_l, :A_A_Δ => A_A_Δ, :B_B_κ => B_B_κ, :A_A_ω => A_A_ω, :B_B_Δ => B_B_Δ, :B_B_ω => B_B_ω, :B_B_l => B_B_l, :A_A_κ => A_A_κ), Dict{Symbol, SecondQuantizedAlgebra.QSym}(:A_a => A_a′, :B_a => B_a′), ["B_in"], ["A_out"], [1.0;;], SecondQuantizedAlgebra.QAdd[(A_A_κ*(A_a)+B_B_κ*(B_a))], (A_A_Δ*(A_a′*A_a)+-0.5A_A_κ*B_B_κ*im*(A_a′*B_a)+B_B_Δ*(B_a′*B_a)+0.5A_A_κ*B_B_κ*im*(A_a*B_a′)))

Overview of SLH systems

The SLH framework represents each open quantum systems by a triple containing:

• S: Scattering matrix describing direct input-output coupling of external (bath) modes
• L: Coupling vector describing the interaction of internal modes with external modes
• H: Hamiltonian describing internal dynamics

Scope of this package

SLHQuantumSystems.jl is for:

• Creating SLH triples (S, L, H) with symbolic parameters (Symbolics.jl) and quantum operators (SecondQuantizedAlgebra.jl).
• Composing named SLH 'blocks' via concatenate and feedbackreduce. Input, output, operator, and parameter names are promoted during composition.
• Converting linear-bosonic SLH systems to state-space form QuantumStateSpace <: ControlSystems.AbstractStateSpace.

Component Library

A small set of reusable components (cavity, squeezing_cavity).

Dependencies

• SecondQuantizedAlgebra.jl provides the symbolic algebra system for quantum operators

References

• This package was inspired by QNET, a python package for working with SLH systems.

• The SLH framework for modeling quantum input-output networks [1]