# 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'].options = '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 = ["X90p:Id"]
gateset_opt_map=[
[
("X90p:Id", "d1", "gauss", "amp"),
],
[
("X90p:Id", "d1", "gauss", "freq_offset"),
],
[
("X90p:Id", "d1", "gauss", "xy_angle"),
],
[
("X90p:Id", "d1", "gauss", "delta"),
]
]


We can look at the parameter values this opt_map specified with

exp.gateset.get_parameters(gateset_opt_map)

[<tf.Tensor: shape=(), dtype=float64, numpy=0.5>,
<tf.Tensor: shape=(), dtype=float64, numpy=-333008821.28051805>,
<tf.Tensor: shape=(), dtype=float64, numpy=-4.440892098500626e-16>,
<tf.Tensor: shape=(), dtype=float64, numpy=0.0>]


More human friendly output is generated by

print(exp.gateset.print_parameters(gateset_opt_map))

X90p:Id-d1-gauss-amp        : 500.000 mV
X90p:Id-d1-gauss-freq_offset: -53.000 MHz 2pi
X90p:Id-d1-gauss-delta      : 0.000

from c3.optimizers.c1 import C1
import c3.libraries.algorithms as algorithms


The C1 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.

opt = C1(
dir_path="/tmp/c3log/",
fid_func=fidelities.average_infid_set,
fid_subspace=["Q1", "Q2"],
gateset_opt_map=gateset_opt_map,
opt_gates=opt_gates,
algorithm=algorithms.lbfgs,
options={"maxfun" : 10},
run_name="better_X90"
)


Finally we supply our defined experiment.

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

0.0006394


And by looking at the same sequences as before.

exp.plot_dynamics(init_state, barely_a_seq, debug=True)

exp.plot_dynamics(init_state, barely_a_seq * 5, debug=True)


Compared to before the optimization.