discretize_stf

Graph.discretize_stf(stf, duration, segment_count, sample_count_per_segment=1, *, name=None)

Create a piecewise-constant function by discretizing a sampleable function.

Use this function to create a piecewise-constant approximation to a sampleable function (obtained, for example, by filtering an initial piecewise-constant function).

Parameters

• stf (Stf) – The sampleable function $v(t)$ to discretize. The values of the function can have any shape. You can also provide a batch of functions, in which case the discretization is applied to each element of the batch.
• duration (float) – The duration $\tau$ over which discretization should be performed. The resulting piecewise-constant function has this duration.
• segment_count (int) – The number of segments $N$ in the resulting piecewise-constant function.
• sample_count_per_segment (int , optional) – The number of samples $M$ of the sampleable function to take when calculating the value of each segment in the discretization. Defaults to 1.
• name (str or None , optional) – The name of the node.

Returns

The piecewise-constant function $w(t)$ obtained by discretizing the sampleable function (or batch of piecewise-constant functions, if you provided a batch of sampleable functions).

Return type

Pwc

SEE ALSO

Graph.convolve_pwc : Create an Stf by convolving a Pwc with a kernel.

Graph.filter_and_resample_pwc : Filter a Pwc with a sinc filter and resample it.

Graph.identity_stf : Create an Stf representing the identity function.

Graph.sample_stf : Sample an Stf at given times.

Notes

The resulting function $w(t)$ is piecewise-constant with $N$ segments, meaning it has segment values $\{w_n\}$ such that $w(t)=w_n$ for $t_{n-1}\leq t\leq t_n$, where $t_n= n \tau/N$.

Each segment value $w_n$ is the average of samples of $v(t)$ at the midpoints of $M$ equally sized subsegments between $t_{n-1}$ and $t_n$:

For more information on Stf nodes see the Working with time-dependent functions in Boulder Opal topic.

Examples

Create discretized Gaussian signal.

>>> times = graph.identity_stf()
>>> gaussian_signal = graph.exp(- (times - 5e-6) ** 2 / 2e-6 ** 2) / 2e-6
>>> discretized_gamma_signal = graph.discretize_stf(
...     stf=gaussian_signal, duration=10e-6, segment_count=256, name="gamma"
... )
>>> discretized_gamma_signal
<Pwc: name="gamma", operation_name="discretize_stf", value_shape=(), batch_shape=()>

Refer to the How to create dephasing and amplitude robust single-qubit gates user guide to find the example in context.