Library

struct EqualityConstraint

Represents a linear equality constraint.

Fields

• ts::AbstractArray{Int}: the time steps at which the constraint is applied
• js::AbstractArray{Int}: the components of the trajectory at which the constraint is applied
• vals::Vector{R}: the values of the constraint
• vardim::Int: the dimension of a single time step of the trajectory
• label::String: a label for the constraint

EqualityConstraint(
    name::Symbol,
    ts::Vector{Int},
    val::Vector{Float64},
    traj::NamedTrajectory;
    label="equality constraint on trajectory variable [name]"
)

Constructs equality constraint for trajectory variable in NamedTrajectory

GlobalEqualityConstraint(
    name::Symbol,
    val::Vector{Float64},
    traj::NamedTrajectory;
    label="equality constraint on global variable [name]"
)::EqualityConstraint

Constructs equality constraint for global variable in NamedTrajectory

dense(vals, structure, shape)

Convert sparse data to dense matrix.

Arguments

• vals: vector of values
• structure: vector of tuples of indices
• shape: tuple of matrix dimensions

show_diffs(A::Matrix, B::Matrix)

Show differences between matrices.

Objective

A structure for defining objective functions.

Fields: L: the objective function ∇L: the gradient of the objective function ∂²L: the Hessian of the objective function ∂²L_structure: the structure of the Hessian of the objective function

GlobalObjective(
    ℓ::Function,
    global_names::AbstractVector{Symbol},
    traj::NamedTrajectory;
    kwargs...
)
GlobalObjective(
    ℓ::Function,
    global_name::Symbol,
    traj::NamedTrajectory;
    kwargs...
)

Create an objective that only involves the global components.

KnotPointObjective(
    ℓ::Function,
    names::AbstractVector{Symbol},
    traj::NamedTrajectory,
    params::AbstractVector;
    kwargs...
)
KnotPointObjective(
    ℓ::Function,
    names::AbstractVector{Symbol},
    traj::NamedTrajectory;
    kwargs...
)
KnotPointObjective(
    ℓ::Function,
    name::Symbol,
    args...;
    kwargs...
)

Create a knot point summed objective function for trajectory optimization, where ℓ(x, p) on trajectory knot point variables x with parameters p. If the parameters argument is omitted, ℓ(x) is assumed to be a function of x only.

Arguments

• ℓ::Function: Function that defines the objective, ℓ(x, p) or ℓ(x).
• names::AbstractVector{Symbol}: Names of the trajectory variables to be optimized.
• traj::NamedTrajectory: The trajectory on which the objective is defined.
• params::AbstractVector: Parameters p for the objective function ℓ, for each time.

Keyword Arguments

• times::AbstractVector{Int}=1:traj.T: Time indices at which the objective is evaluated.
• Qs::AbstractVector{Float64}=ones(traj.T): Weights for the objective function at each time.

MinimumTimeObjective

A type of objective that counts the time taken to complete a task. D is a scaling factor.

QuadraticRegularizer

A quadratic regularizer for a trajectory component.

Fields: name: the name of the trajectory component to regularize traj: the trajectory R: the regularization matrix diagonal baseline: the baseline values for the trajectory component times: the times at which to evaluate the regularizer

TrajectoryDynamics

A struct for trajectory optimization dynamics, represented by integrators that compute single time step dynamics, and functions for jacobians and hessians.

Fields

• integrators::Union{Nothing, Vector{<:AbstractIntegrator}}: Vector of integrators.
• F!::Function: Function to compute trajectory dynamics.
• ∂F!::Function: Function to compute the Jacobian of the dynamics.
• ∂fs::Vector{SparseMatrixCSC{Float64, Int}}: Vector of Jacobian matrices.
• μ∂²F!::Union{Function, Nothing}: Function to compute the Hessian of the Lagrangian.
• μ∂²fs::Vector{SparseMatrixCSC{Float64, Int}}: Vector of Hessian matrices.
• dim::Int: Total dimension of the dynamics.

mutable struct DirectTrajOptProblem <: AbstractProblem

Stores all the information needed to set up and solve a DirectTrajOptProblem as well as the solution after the solver terminates.

Fields

• optimizer::Ipopt.Optimizer: Ipopt optimizer object

trajectory_constraints(traj::NamedTrajectory)

Implements the initial and final value constraints and bounds constraints on the controls and states as specified by traj.

Solver options for Ipopt

https://coin-or.github.io/Ipopt/OPTIONS.html#OPT_print_options_documentation

solve!(prob::DirectTrajOptProblem; inittraj=nothing, savepath=nothing, maxiter=prob.ipoptoptions.maxiter, linearsolver=prob.ipoptoptions.linearsolver, printlevel=prob.ipoptoptions.printlevel, removeslackvariables=false, callback=nothing # statetype=:unitary, # print_fidelity=false, )

Call optimization solver to solve the quantum control problem with parameters and callbacks.

Arguments

• prob::DirectTrajOptProblem: The quantum control problem to solve.
• init_traj::NamedTrajectory: Initial guess for the control trajectory. If not provided, a random guess will be generated.
• save_path::String: Path to save the problem after optimization.
• max_iter::Int: Maximum number of iterations for the optimization solver.
• linear_solver::String: Linear solver to use for the optimization solver (e.g., "mumps", "paradiso", etc).
• print_level::Int: Verbosity level for the solver.
• callback::Function: Callback function to call during optimization steps.