Open-loop optimal controlΒΆ

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-xy_angle   : -444.089 arad
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()
_images/output_84_1.png _images/output_84_3.png

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)
_images/output_88_0.png
exp.plot_dynamics(init_state, barely_a_seq * 5, debug=True)
_images/output_89_0.png

Compared to before the optimization.

_images/dyn_5X.png