Problem Templates Overview

QuantumCollocation.jl provides 4 problem templates that cover common quantum optimal control scenarios. These templates make it easy to set up and solve problems without manually constructing objectives, constraints, and integrators.

Template Comparison

Template	Objective	Time	Use Case
`SmoothPulseProblem`	Minimize control effort + infidelity	Fixed	Standard gate/state synthesis with smooth pulses
`MinimumTimeProblem`	Minimize duration	Variable	Fastest gate/state synthesis given fidelity constraint
`SplinePulseProblem`	Minimize control effort + infidelity	Fixed	Gate/state synthesis with spline-based pulses (linear or cubic Hermite)
`SamplingProblem`	Minimize control effort + weighted sum of infidelity objectives	Fixed	Robust gate/state synthesis where the controls are shared across all systems, with differing dynamics.

Smooth Pulse vs Minimum Time

Smooth Pulse: Fixed total time T × Δt, minimizes control effort with regularization on u, u̇, ü
Minimum Time: Variable timesteps Δt[k], minimizes total duration subject to fidelity constraint

Sampling Problems

Solve for a single control pulse that works well across multiple quantum systems
Useful for robustness against parameter uncertainties or manufacturing variations
Examples: different coupling strengths, detunings, or environmental conditions

Quick Selection Guide

I want to implement a quantum gate:

Start simple? → SmoothPulseProblem + UnitaryTrajectory
Need speed? → MinimumTimeProblem + UnitaryTrajectory
Need robustness? → SamplingProblem + UnitaryTrajectory

I want to prepare a quantum state:

Standard case? → SmoothPulseProblem + KetTrajectory
Speed critical? → MinimumTimeProblem + KetTrajectory
Robust preparation? → SamplingProblem + KetTrajectory

Common Parameters

All templates share these key parameters:

prob = SmoothPulseProblem(
    qtraj,              # QuantumTrajectory wrapping system information, Unitary/Ket/MultiKet problem type
    N;                  # Number of timesteps

    Q=100.0,            # Objective weighting coefficient for the infidelity
    R=1e-2,             # Objective weighting coefficient for the controls regularization

    piccolo_options = PiccoloOptions(verbose = true),  # PiccoloOptions for solver configuration
)

QuantumControlProblem{PiccoloQuantumObjects.QuantumTrajectories.UnitaryTrajectory{PiccoloQuantumObjects.Pulses.ZeroOrderPulse{DataInterpolations.ConstantInterpolation{Matrix{Float64}, Vector{Float64}, Vector{Union{}}, Float64}}, SciMLBase.ODESolution{ComplexF64, 3, Vector{Matrix{ComplexF64}}, Nothing, Nothing, Vector{Float64}, Vector{Vector{Matrix{ComplexF64}}}, Nothing, SciMLBase.ODEProblem{Matrix{ComplexF64}, Tuple{Float64, Float64}, true, SciMLBase.NullParameters, SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, SciMLOperators.MatrixOperator{ComplexF64, Matrix{ComplexF64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{PiccoloQuantumObjects.Rollouts.var"#update!#_construct_operator##2"{PiccoloQuantumObjects.QuantumSystems.QuantumSystem{PiccoloQuantumObjects.QuantumSystems.var"#26#27"{SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, Vector{SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, Int64}, PiccoloQuantumObjects.QuantumSystems.var"#28#29"{Vector{SparseArrays.SparseMatrixCSC{Float64, Int64}}, Int64, SparseArrays.SparseMatrixCSC{Float64, Int64}}, @NamedTuple{}}}, Val{()}}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, PiccoloQuantumObjects.Rollouts.PiccoloRolloutSystem{Union{Int64, AbstractVector{Int64}, CartesianIndex, CartesianIndices}}, Nothing, Nothing}, Base.Pairs{Symbol, Vector{Float64}, Nothing, @NamedTuple{tstops::Vector{Float64}, saveat::Vector{Float64}}}, SciMLBase.StandardODEProblem}, OrdinaryDiffEqLinear.MagnusGL4, OrdinaryDiffEqCore.InterpolationData{SciMLBase.ODEFunction{true, SciMLBase.FullSpecialize, SciMLOperators.MatrixOperator{ComplexF64, Matrix{ComplexF64}, SciMLOperators.FilterKwargs{Nothing, Val{()}}, SciMLOperators.FilterKwargs{PiccoloQuantumObjects.Rollouts.var"#update!#_construct_operator##2"{PiccoloQuantumObjects.QuantumSystems.QuantumSystem{PiccoloQuantumObjects.QuantumSystems.var"#26#27"{SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, Vector{SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, Int64}, PiccoloQuantumObjects.QuantumSystems.var"#28#29"{Vector{SparseArrays.SparseMatrixCSC{Float64, Int64}}, Int64, SparseArrays.SparseMatrixCSC{Float64, Int64}}, @NamedTuple{}}}, Val{()}}}, LinearAlgebra.UniformScaling{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED), Nothing, PiccoloQuantumObjects.Rollouts.PiccoloRolloutSystem{Union{Int64, AbstractVector{Int64}, CartesianIndex, CartesianIndices}}, Nothing, Nothing}, Vector{Matrix{ComplexF64}}, Vector{Float64}, Vector{Vector{Matrix{ComplexF64}}}, Nothing, OrdinaryDiffEqLinear.MagnusGL4Cache{Matrix{ComplexF64}, Matrix{ComplexF64}, Matrix{ComplexF64}, Nothing}, Nothing}, SciMLBase.DEStats, Nothing, Nothing, Nothing, Nothing}, Matrix{ComplexF64}}}
  System: PiccoloQuantumObjects.QuantumSystems.QuantumSystem{PiccoloQuantumObjects.QuantumSystems.var"#26#27"{SparseArrays.SparseMatrixCSC{ComplexF64, Int64}, Vector{SparseArrays.SparseMatrixCSC{ComplexF64, Int64}}, Int64}, PiccoloQuantumObjects.QuantumSystems.var"#28#29"{Vector{SparseArrays.SparseMatrixCSC{Float64, Int64}}, Int64, SparseArrays.SparseMatrixCSC{Float64, Int64}}, @NamedTuple{}}
  Goal: Matrix{ComplexF64}
  Trajectory: 51 knots
  State: Ũ⃗
  Controls: u

See the individual template pages for parameter details and examples.

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