2.2. Modelling an Advanced TablePulseTemplate

The SimpleTablePulse example shows how a simple parametrized TablePT on one channel can implemented and how the interpolation works.

This example demonstrates how to set up a more complex TablePT. This means we will include multiple channels and use expressions for times and voltages.

First lets reimplement the pulse from the previous example but this time with a second channel 'B', that has the same voltage values but negative. To do this, we extend the entry dict by a second item with the channel ID 'B' as key and the entry list as value.

Then we plot it to see that it actually works.

%matplotlib notebook
from qupulse.pulses.plotting import plot
from qupulse.pulses import TablePT

param_entries = {'A': [(0, 0),
                       ('ta', 'va', 'hold'),
                       ('tb', 'vb', 'linear'),
                       ('tend', 0, 'jump')],
                 'B': [(0, 0),
                       ('ta', '-va', 'hold'),
                       ('tb', '-vb', 'linear'),
                       ('tend', 0, 'jump')]}
mirror_pulse = TablePT(param_entries)

parameters = {'ta': 2,
              'va': 2,
              'tb': 4,
              'vb': 3,
              'tend': 6}

_ = plot(mirror_pulse, parameters, sample_rate=100)

You may have noticed that we already used an expression in the entry list: '-va' and '-vb'. Of course we can also do a bit more complex things with these than a simple negation. Let’s have a look at the next example where we use some simple mathematical oeprators and built-in functions:

expr_pulse = TablePT({'A': [(0,     'a_0'),
                            ('t_1', 'a_0 + exp(theta)', 'hold'),
                            ('t_2', 'Abs(x_0 - y_0)', 'linear')],
                      'B': [(0,               'b_0'),
                            ('t_1*(b_0/a_0)', 'b_1', 'linear'),
                            ('t_2',           'b_2')]})
_ = plot(expr_pulse, dict(a_0=1.1, theta=2, x_0=0.5, y_0=1, t_1=10, t_2=25, b_0=0.6, b_1=6, b_2=0.4))

Is there a requirement that all channels have the same duration?

No. The shorter channels stay on their last value until the last channel is finished. The duration of the complete pulse template is given as the corresponding expression:

param_entries = {'A': [(0, 0),
                       ('t_A/2', 'va', 'hold'),
                       ('t_A', 'vb', 'linear')],
                 'B': [(0, 0),
                       ('t_B / 2', 'va', 'hold'),
                       ('t_B', 'vb', 'linear')]}

c_pulse = TablePT(param_entries)
print(c_pulse.duration)
_ = plot(c_pulse, dict(t_A=4, t_B=5, va=1, vb=2, t_wait = 2), sample_rate=100)

Max(t_A, t_B)

As you see channel 'A' only was defined until 4ns and holds this level to the end of the pulse.