pwc

Graph.pwc(durations, values, time_dimension=0, *, name=None)

Create a piecewise-constant function of time.

Parameters

• durations (np.ndarray ( 1D , real )) – The durations $\{\delta t_n\}$ of the $N$ constant segments.
• values (np.ndarray or Tensor) – The values $\{v_n\}$ of the function on the constant segments. The dimension corresponding to time_dimension must be the same length as durations. To create a batch of $B_1 \times \ldots \times B_n$ piecewise-constant tensors of shape $D_1 \times \ldots \times D_m$, provide this values parameter as an object of shape $B_1\times\ldots\times B_n\times N\times D_1\times\ldots\times D_m$.
• time_dimension (int , optional) – The axis along values corresponding to time. All dimensions that come before the time_dimension are batch dimensions: if there are $n$ batch dimensions, then time_dimension is also $n$. Defaults to 0, which corresponds to no batch. Note that you can pass a negative value to refer to the time dimension.
• name (str or None , optional) – The name of the node.

Returns

The piecewise-constant function of time $v(t)$, satisfying $v(t)=v_n$ for $t_{n-1}\leq t\leq t_n$, where $t_0=0$ and $t_n=t_{n-1}+\delta t_n$. If you provide a batch of values, the returned Pwc represents a corresponding batch of $B_1 \times \ldots \times B_n$ functions $v(t)$, each of shape $D_1 \times \ldots \times D_m$.

Return type

Pwc

SEE ALSO

Graph.pwc_operator : Create Pwc operators.

Graph.pwc_signal : Create Pwc signals from (possibly complex) values.

Graph.pwc_sum : Sum multiple Pwcs.

Notes

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

Examples

Create a Hamiltonian from a piecewise-constant signal with non-uniform segment durations.

>>> omega = graph.pwc(
...     values=np.array([1, 2, 3]), durations=np.array([0.1, 0.2, 0.3]), name="omega"
... )
>>> omega
<Pwc: name="omega", operation_name="pwc", value_shape=(), batch_shape=()>
>>> sigma_z = np.array([[1, 0], [0, -1]])
>>> hamiltonian = omega * sigma_z
>>> hamiltonian.name = "hamiltonian"
>>> result = bo.execute_graph(graph=graph, output_node_names="hamiltonian")
>>> result["output"]["hamiltonian"]
{
    'durations': array([0.1, 0.2, 0.3]),
    'values': array([
        [[ 1.,  0.], [ 0., -1.]],
        [[ 2.,  0.], [ 0., -2.]],
        [[ 3.,  0.], [ 0., -3.]]
    ]),
    'time_dimension': 0
}

See more examples in the How to simulate quantum dynamics subject to noise with graphs user guide.