Open-loop optimal control

In order to improve the gate from the previous example Setup of a two-qubit chip with C^3, we create the optimizer object for open-loop optimal control. Examining the previous dynamics .. image:: dyn_singleX.png

in addition to over-rotation, we notice some leakage into the \(|2,0>\) state and enable a DRAG option. Details on DRAG can be found here. The main principle is adding a phase-shifted component proportional to the derivative of the original signal. With automatic differentiation, our AWG can perform this operation automatically for arbitrary shapes.

generator.devices['AWG'].enable_drag_2()

At the moment there are two implementations of DRAG, variant 2 is independent of the AWG resolution.

To define which parameters we optimize, we write the gateset_opt_map, a nested list of tuples that identifies each parameter.

opt_gates = ["rx90p[0]"]
gateset_opt_map=[
    [
      ("rx90p[0]", "d1", "gauss", "amp"),
    ],
    [
      ("rx90p[0]", "d1", "gauss", "freq_offset"),
    ],
    [
      ("rx90p[0]", "d1", "gauss", "xy_angle"),
    ],
    [
      ("RX90p:Id", "d1", "gauss", "delta"),
    ]
]
parameter_map.set_opt_map(gateset_opt_map)

We can look at the parameter values this opt_map specified with

parameter_map.print_parameters()

rx90p[0]-d1-gauss-amp                 : 500.000 mV
rx90p[0]-d1-gauss-freq_offset         : -53.000 MHz 2pi
rx90p[0]-d1-gauss-xy_angle            : -444.089 arad
rx90p[0]-d1-gauss-delta               : -1.000

from c3.optimizers.optimalcontrol import OptimalControl
import c3.libraries.algorithms as algorithms

The OptimalControl object will handle the optimization for us. As a fidelity function we choose average fidelity as well as LBFG-S (a wrapper of the scipy implementation) from our library. See those libraries for how these functions are defined and how to supply your own, if necessary.

import os
import tempfile

# Create a temporary directory to store logfiles, modify as needed
log_dir = os.path.join(tempfile.TemporaryDirectory().name, "c3logs")

opt = OptimalControl(
    dir_path=log_dir,
    fid_func=fidelities.average_infid_set,
    fid_subspace=["Q1", "Q2"],
    pmap=parameter_map,
    algorithm=algorithms.lbfgs,
    options={"maxfun" : 10},
    run_name="better_X90"
)

Finally we supply our defined experiment.

exp.set_opt_gates(opt_gates)
opt.set_exp(exp)

Everything is in place to start the optimization.

opt.optimize_controls()

After a few steps we have improved the gate significantly, as we can check with

opt.current_best_goal

0.00063

And by looking at the same sequences as before.

plot_dynamics(exp, init_state, barely_a_seq)

plot_dynamics(exp, init_state, barely_a_seq * 5)

Compared to before the optimization.