The work flow for solving a quantum optimal control problem consists of the following general steps:

1. Setup
2. Optimize
3. Visualize the results

1. Setup

The setup phase includes specifying

• The size of the state vector
• The system and control Hamiltonians
• The target gate transformation
• Duration of the gate and number of time steps for integrating Schroedinger's equation.

For the parameterization of the control functions, you need to specify

• Carrier wave frequencies
• Number of B-spline coefficients in each spline

The properties of the control problem are stored in a mutable struct that is populated by calling

• params = Juqbox.objparams().

The next steps are:

• Assign the initial parameter vector (called pcof0 in the examples below)
• Set bounds for the parameter vector to be imposed during the optimization
• Allocate working arrays by calling wa = Juqbox.Working_arrays()
• Assign convergence criteria and other parameters for the optimizer
• Build the optimization structure by calling prob = Juqbox.setup_ipopt_problem()

2. Optimization

Once you have been assigned the params and prob objects, as well as the initial parameter vector pcof0, the optimizer is invoked by

• pcof = Juqbox.run_optimizer(prob, pcof0)

3. Visualizing the results

General properties of the optimized solution such as trace infidelity and unitary accuracy can be evaluated, and a number of figures can generated by invoking

• pl = Juqbox.plot_results(params, pcof)

An array of Julia plot objects is returned in pl. These objects can be visualized on the screen

• display(pl[1])

where pl[1] is the first Julia plot object. The following plot objects are populated by the script:

• pl[1] Evolution of the state vector population
• pl[2] Control functions in the rotating frame of reference
• pl[3] Population of forbidden energy levels
• pl[4] Lab frame control function(s)
• pl[5] Fourier transform of the lab-frame control functions (linear scale)
• pl[6] Fourier transform of the lab-frame control functions (log scale)
• pl[7] Coefficients of the optimized parameter vector
• pl[8] Convergence of the optimization