Add analytic pulse function samplers (Qiskit#2042)

* Update remote simulator test for backend IBMQ/Aer changes

* Added test module and case for samplers.

* Added base sampling decorator along with left, right, and midpoint samplers

* Added tests to samplers.

* change FunctionalPulse to decorator

* update error function and imports

* update unittest

* add functools.wraps

* remove getter, setter from sample pulse

* fix lint

* Added dynamic updating of docstrings for decorated sampled functions.

* Added explicit documentation for standard library samplers.

* Added extensive sampler module docstring for developers.

* Update changelog with sampler.

* Separate standard library and external libraries

* Updated changelog for functional_pulse.

* update sampler for functional_pulse decorator. Add additional tests.

* Changed all instances of 'analytic' to 'continuous'

* Update sampler module structure to separate sampling functions and decorators.

* Remove sampler prefix to sampler module's modules.

* Update small bug from rename

* Change dtype casting to np.complex_

* remove accidental remote simulator file.

* Removed required default parameters.

* Update changelog. Update defaults model validation to add nonetypes.

* Update changelog.

* Readd parameters to be required.

* Update docstring and delete extra function following review.

CHANGELOG.rst

@@ -80,6 +80,7 @@ Added
 Changed
 -------
 
+- Backend defaults values are no longer required (#2101).
 - QuantumCircuit properties more self-consistent and no longer need DAG (#1993).
 - The most connected subset in DenseLayout is now reduced bandwidth (#2021).
 - plot_histogram now allows sorting by Hamming distance from target_string (#2064).

qiskit/pulse/samplers/__init__.py

@@ -0,0 +1,10 @@
+# -*- coding: utf-8 -*-
+
+# Copyright 2019, IBM.
+#
+# This source code is licensed under the Apache License, Version 2.0 found in
+# the LICENSE.txt file in the root directory of this source tree.
+
+"""Module for Samplers."""
+
+from .decorators import *

qiskit/pulse/samplers/decorators.py

@@ -0,0 +1,269 @@
+# -*- coding: utf-8 -*-
+
+# Copyright 2019, IBM.
+#
+# This source code is licensed under the Apache License, Version 2.0 found in
+# the LICENSE.txt file in the root directory of this source tree.
+
+# pylint: disable=missing-return-doc
+
+"""Sampler decorator module for sampling of continuous pulses to discrete pulses to be
+exposed to user.
+
+Some atypical boilerplate has been added to solve the problem of decorators not preserving
+their wrapped function signatures. Below we explain the problem that samplers solve and how
+we implement this.
+
+A sampler is a function that takes an continuous pulse function with signature:
+    ```python
+    def f(times: np.ndarray, *args, **kwargs) -> np.ndarray:
+        ...
+    ```
+and returns a new function:
+    def f(duration: int, *args, **kwargs) -> SamplePulse:
+        ...
+
+Samplers are used to build up pulse commands from continuous pulse functions.
+
+In Python the creation of a dynamic function that wraps another function will cause
+the underlying signature and documentation of the underlying function to be overwritten.
+In order to circumvent this issue the Python standard library provides the decorator
+`functools.wraps` which allows the programmer to expose the names and signature of the
+wrapped function as those of the dynamic function.
+
+Samplers are implemented by creating a function with signature
+    @sampler
+    def left(continuous_pulse: Callable, duration: int, *args, **kwargs)
+        ...
+
+This will create a sampler function for `left`. Since it is a dynamic function it would not
+have the docstring of `left` available too `help`. This could be fixed by wrapping with
+`functools.wraps` in the `sampler`, but this would then cause the signature to be that of the
+sampler function which is called on the continuous pulse, below:
+    `(continuous_pulse: Callable, duration: int, *args, **kwargs)``
+This is not correct for the sampler as the output sampled functions accept only a function.
+For the standard sampler we get around this by not using `functools.wraps` and
+explicitly defining our samplers such as `left`, `right` and `midpoint` and
+calling `sampler` internally on the function that implements the sampling schemes such as
+`left_sample`, `right_sample` and `midpoint_sample` respectively. See `left` for an example of this.
+
+In this way our standard samplers will expose the proper help signature, but a user can
+still create their own sampler with
+    @sampler
+    def custom_sampler(time, *args, **kwargs):
+        ...
+However, in this case it will be missing documentation of the underlying sampling methods.
+We believe that the definition of custom samplers will be rather infrequent.
+
+However, users will frequently apply sampler instances too continuous pulses. Therefore, a different
+approach was required for sampled continuous functions (the output of an continuous pulse function
+decorated by a sampler instance).
+
+A sampler instance is a decorator that may be used to wrap continuous pulse functions such as
+linear below:
+```python
+    @left
+    def linear(times: np.ndarray, m: float, b: float) -> np.ndarray:
+        ```Linear test function
+        Args:
+            times: Input times.
+            m: Slope.
+            b: Intercept
+        Returns:
+            np.ndarray
+        ```
+        return m*times+b
+```
+Which after decoration may be called with a duration rather than an array of times
+    ```python
+    duration = 10
+    pulse_command = linear(10, 0.1, 0.1)
+    ```
+If one calls help on `linear` they will find
+    ```
+    linear(duration:int, *args, **kwargs) -> numpy.ndarray
+    Discretized continuous pulse function: `linear` using
+    sampler: `_left`.
+
+     The first argument (time) of the continuous pulse function has been replaced with
+     a discretized `duration` of type (int).
+
+     Args:
+         duration (int)
+         *args: Remaining arguments of continuous pulse function.
+                See continuous pulse function documentation below.
+         **kwargs: Remaining kwargs of continuous pulse function.
+                   See continuous pulse function documentation below.
+
+     Sampled continuous function:
+
+        function linear in module test.python.pulse.test_samplers
+        linear(x:numpy.ndarray, m:float, b:float) -> numpy.ndarray
+            Linear test function
+            Args:
+                x: Input times.
+                m: Slope.
+                b: Intercept
+            Returns:
+                np.ndarray
+    ```
+This is partly because `functools.wraps` has been used on the underlying function.
+This in itself is not sufficient as the signature of the sampled function has
+`duration`, whereas the signature of the continuous function is `time`.
+
+This is acheived by removing `__wrapped__` set by `functools.wraps` in order to preserve
+the correct signature and also applying `_update_annotations` and `_update_docstring`
+to the generated function which corrects the function annotations and adds an informative
+docstring respectively.
+
+The user therefore has access to the correct sampled function docstring in its entirety, while
+still seeing the signature for the continuous pulse function and all of its arguments.
+"""
+
+import functools
+from typing import Callable
+import textwrap
+import pydoc
+
+import numpy as np
+
+from qiskit.pulse.samplers import strategies
+import qiskit.pulse.commands as commands
+
+
+def _update_annotations(discretized_pulse: Callable) -> Callable:
+    """Update annotations of discretized continuous pulse function with duration.
+
+    Args:
+        discretized_pulse: Discretized decorated continuous pulse.
+    """
+    undecorated_annotations = list(discretized_pulse.__annotations__.items())
+    decorated_annotations = undecorated_annotations[1:]
+    decorated_annotations.insert(0, ('duration', int))
+    discretized_pulse.__annotations__ = dict(decorated_annotations)
+    return discretized_pulse
+
+
+def _update_docstring(discretized_pulse: Callable, sampler_inst: Callable) -> Callable:
+    """Update annotations of discretized continuous pulse function.
+
+    Args:
+        discretized_pulse: Discretized decorated continuous pulse.
+        sampler_inst: Applied sampler.
+    """
+    wrapped_docstring = pydoc.render_doc(discretized_pulse, '%s')
+    header, body = wrapped_docstring.split('\n', 1)
+    body = textwrap.indent(body, '                    ')
+    wrapped_docstring = header+body
+    updated_ds = """
+                Discretized continuous pulse function: `{continuous_name}` using
+                sampler: `{sampler_name}`.
+
+                 The first argument (time) of the continuous pulse function has been replaced with
+                 a discretized `duration` of type (int).
+
+                 Args:
+                     duration (int)
+                     *args: Remaining arguments of continuous pulse function.
+                            See continuous pulse function documentation below.
+                     **kwargs: Remaining kwargs of continuous pulse function.
+                               See continuous pulse function documentation below.
+
+                 Sampled continuous function:
+
+                    {continuous_doc}
+                """.format(continuous_name=discretized_pulse.__name__,
+                           sampler_name=sampler_inst.__name__,
+                           continuous_doc=wrapped_docstring)
+
+    discretized_pulse.__doc__ = updated_ds
+    return discretized_pulse
+
+
+def sampler(sample_function: Callable) -> Callable:
+    """Sampler decorator base method.
+
+    Samplers are used for converting an continuous function to a discretized pulse.
+
+    They operate on a function with the signature:
+        `def f(times: np.ndarray, *args, **kwargs) -> np.ndarray`
+    Where `times` is a numpy array of floats with length n_times and the output array
+    is a complex numpy array with length n_times. The output of the decorator is an
+    instance of `FunctionalPulse` with signature:
+        `def g(duration: int, *args, **kwargs) -> SamplePulse`
+
+    Note if your continuous pulse function outputs a `complex` scalar rather than a
+    `np.ndarray`, you should first vectorize it before applying a sampler.
+
+    This class implements the sampler boilerplate for the sampler.
+
+    Args:
+        sample_function: A sampler function to be decorated.
+    """
+
+    def generate_sampler(continuous_pulse: Callable) -> Callable:
+        """Return a decorated sampler function."""
+
+        @functools.wraps(continuous_pulse)
+        def call_sampler(duration: int, *args, **kwargs) -> commands.SamplePulse:
+            """Replace the call to the continuous function with a call to the sampler applied
+            to the anlytic pulse function."""
+            sampled_pulse = sample_function(continuous_pulse, duration, *args, **kwargs)
+            return np.asarray(sampled_pulse, dtype=np.complex_)
+
+        # Update type annotations for wrapped continuous function to be discrete
+        call_sampler = _update_annotations(call_sampler)
+        # Update docstring with that of the sampler and include sampled function documentation.
+        call_sampler = _update_docstring(call_sampler, sample_function)
+        # Unset wrapped to return base sampler signature
+        # but still get rest of benefits of wraps
+        # such as __name__, __qualname__
+        call_sampler.__dict__.pop('__wrapped__')
+        # wrap with functional pulse
+        return commands.functional_pulse(call_sampler)
+
+    return generate_sampler
+
+
+def left(continuous_pulse: Callable) -> Callable:
+    r"""Left sampling strategy decorator.
+
+    See `pulse.samplers.sampler` for more information.
+
+    For `duration`, return:
+        $$\{f(t) \in \mathbb{C} | t \in \mathbb{Z} \wedge  0<=t<\texttt{duration}\}$$
+
+    Args:
+        continuous_pulse: To sample.
+    """
+
+    return sampler(strategies.left_sample)(continuous_pulse)
+
+
+def right(continuous_pulse: Callable) -> Callable:
+    r"""Right sampling strategy decorator.
+
+    See `pulse.samplers.sampler` for more information.
+
+    For `duration`, return:
+        $$\{f(t) \in \mathbb{C} | t \in \mathbb{Z} \wedge  0<t<=\texttt{duration}\}$$
+
+    Args:
+        continuous_pulse: To sample.
+    """
+
+    return sampler(strategies.right_sample)(continuous_pulse)
+
+
+def midpoint(continuous_pulse: Callable) -> Callable:
+    r"""Midpoint sampling strategy decorator.
+
+    See `pulse.samplers.sampler` for more information.
+
+    For `duration`, return:
+        $$\{f(t+0.5) \in \mathbb{C} | t \in \mathbb{Z} \wedge  0<=t<\texttt{duration}\}$$
+
+    Args:
+        continuous_pulse: To sample.
+    """
+    return sampler(strategies.midpoint_sample)(continuous_pulse)

qiskit/pulse/samplers/strategies.py

@@ -0,0 +1,64 @@
+# -*- coding: utf-8 -*-
+
+# Copyright 2019, IBM.
+#
+# This source code is licensed under the Apache License, Version 2.0 found in
+# the LICENSE.txt file in the root directory of this source tree.
+
+# pylint: disable=missing-return-doc
+
+"""Sampler strategy module for sampler functions.
+
+Sampler functions have signature.
+    ```python
+    def sampler_function(continuous_pulse: Callable, duration: int, *args, **kwargs) -> np.ndarray:
+        ...
+    ```
+where the supplied `continuous_pulse` is a function with signature:
+    ```python
+    def f(times: np.ndarray, *args, **kwargs) -> np.ndarray:
+        ...
+    ```
+The sampler will call the `continuous_pulse` function with a set of times it will decide
+according to the sampling strategy it implments along with the passed `args` and `kwargs`.
+"""
+
+from typing import Callable
+
+import numpy as np
+
+
+def left_sample(continuous_pulse: Callable, duration: int, *args, **kwargs) -> np.ndarray:
+    """Left sample a continuous function.
+    Args:
+        continuous_pulse: Continuous pulse function to sample.
+        duration: Duration to sample for.
+        *args: Continuous pulse function args.
+        **kwargs: Continuous pulse function kwargs.
+    """
+    times = np.arange(duration)
+    return continuous_pulse(times, *args, **kwargs)
+
+
+def right_sample(continuous_pulse: Callable, duration: int, *args, **kwargs) -> np.ndarray:
+    """Sampling strategy for decorator.
+    Args:
+        continuous_pulse: Continuous pulse function to sample.
+        duration: Duration to sample for.
+        *args: Continuous pulse function args.
+        **kwargs: Continuous pulse function kwargs.
+    """
+    times = np.arange(1, duration+1)
+    return continuous_pulse(times, *args, **kwargs)
+
+
+def midpoint_sample(continuous_pulse: Callable, duration: int, *args, **kwargs) -> np.ndarray:
+    """Sampling strategy for decorator.
+    Args:
+        continuous_pulse: Continuous pulse function to sample.
+        duration: Duration to sample for.
+        *args: Continuous pulse function args.
+        **kwargs: Continuous pulse function kwargs.
+    """
+    times = np.arange(1/2, duration + 1/2)
+    return continuous_pulse(times, *args, **kwargs)