`Open Quantum Systems`

using PiccoloQuantumObjects
using SparseArrays # for visualization

Open quantum systems

We can construct an OpenQuantumSystem with Lindblad dynamics, enabling a user to pass a list of dissipation operators.

PiccoloQuantumObjects.QuantumSystems.OpenQuantumSystem — Type

OpenQuantumSystem <: AbstractQuantumSystem

A struct for storing open quantum dynamics.

Fields

H::Function: The Hamiltonian function: (u, t) -> H(u, t)
𝒢::Function: The Lindbladian generator function: u -> 𝒢(u)
H_drift::SparseMatrixCSC{ComplexF64, Int}: The drift Hamiltonian
H_drives::Vector{SparseMatrixCSC{ComplexF64, Int}}: The drive Hamiltonians
T_max::Float64: Maximum evolution time
drive_bounds::Vector{Tuple{Float64, Float64}}: Drive amplitude bounds
n_drives::Int: The number of control drives
levels::Int: The number of levels in the system
dissipation_operators::Vector{SparseMatrixCSC{ComplexF64, Int}}: The dissipation operators
time_dependent::Bool: Whether the Hamiltonian has explicit time dependence

See also QuantumSystem.

source

Add a dephasing and annihilation error channel.

H_drives = [PAULIS[:X]]
a = annihilate(2)
dissipation_operators = [a'a, a]
T_max = 10.0
drive_bounds = [(-1.0, 1.0)]
system = OpenQuantumSystem(H_drives, T_max, drive_bounds, dissipation_operators=dissipation_operators)
system.dissipation_operators[1] |> sparse

2×2 SparseArrays.SparseMatrixCSC{ComplexF64, Int64} with 1 stored entry:
     ⋅          ⋅    
     ⋅      1.0+0.0im

system.dissipation_operators[2] |> sparse

2×2 SparseArrays.SparseMatrixCSC{ComplexF64, Int64} with 1 stored entry:
     ⋅      1.0+0.0im
     ⋅          ⋅

Warning

The Hamiltonian part system.H excludes the Lindblad operators. This is also true for functions that report properties of system.H, such as get_drift, get_drives, and is_reachable.

get_drift(system) |> sparse

2×2 SparseArrays.SparseMatrixCSC{ComplexF64, Int64} with 0 stored entries:
     ⋅          ⋅    
     ⋅          ⋅

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