complex_pwc_signal

Graph.complex_pwc_signal(moduli, phases, duration, *, name=None)

Create a complex piecewise-constant signal from moduli and phases.

Use this function to create a complex piecewise-constant signal from moduli and phases defined for each segment, in which the constant segments all have the same duration.

Parameters:

moduli (np.ndarray(real) or Tensor(real)) – The moduli \(\{\Omega_n\}\) of the values of \(N\) constant segments. These can represent either the moduli of a single sequence of segment values or of a batch of them. To provide a batch of sequences of segment values of shape \(B_1 \times \ldots \times B_n\), represent these moduli as a tensor of shape \(B_1 \times \ldots \times B_n \times N\).
phases (np.ndarray(real) or Tensor(real)) – The phases \(\{\phi_n\}\) of the complex segment values. Must have the same length as moduli (or same shape, if you’re providing a batch).
duration (float) – The total duration \(\tau\) of the signal.
name (str or None, optional) – The name of the node.

Returns:

The piecewise-constant function of time \(v(t)\), satisfying \(v(t)=\Omega_n e^{i\phi_n}\) for \(t_{n-1}\leq t\leq t_n\), where \(t_n=n\tau/N\) (where \(N\) is the number of values in \(\{\Omega_n\}\) and \(\{\phi_n\}\)). If you provide a batch of moduli and phases, the returned Pwc represents a corresponding batch of \(B_1 \times \ldots \times B_n\) functions \(v(t)\).

Return type:

Pwc(complex)

See also

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

Notes

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

Examples

Create a complex piecewise-constant signal with batched moduli and phases.

>>> moduli = np.array([[1, 2], [3, 4]])
>>> phases = np.array([[0.1, 0.2], [0.5, 0.7]])
>>> graph.complex_pwc_signal(moduli=moduli, phases=phases, duration=0.2, name="signal")
<Pwc: name="signal", operation_name="complex_pwc_signal", value_shape=(), batch_shape=(2,)>
>>> result = qctrl.functions.calculate_graph(graph=graph, output_node_names=["signal"])
>>> result.output["signal"]
[
    [
        {"value": (0.9950041652780258 + 0.09983341664682815j), "duration": 0.1},
        {"value": (1.9601331556824833 + 0.39733866159012243j), "duration": 0.1},
    ],
    [
        {"value": (2.6327476856711183 + 1.438276615812609j), "duration": 0.1},
        {"value": (3.059368749137954 + 2.576870748950764j), "duration": 0.1},
    ],
]

See more examples in the Design robust single-qubit gates using computational graphs tutorial.