Add qml.generator(op) function (#2256)

* Add operator transform functionality

* Add matrix function:

* add tests

* add tests

* add tests

* add tests

* add tests

* add tests

* add tests

* more docs

* more

* add tests

* Apply suggestions from code review

Co-authored-by: Maria Schuld <mariaschuld@gmail.com>

* Add qml.eigval() function

* add test

* finish adding tests

* finish adding tests

* Add qml.generator(op) function

* fixes

* more tests

* more tests

* fix

* more tests

* Apply suggestions from code review

Co-authored-by: Maria Schuld <mariaschuld@gmail.com>

* Apply suggestions from code review

Co-authored-by: Maria Schuld <mariaschuld@gmail.com>

* Update tests/ops/functions/test_eigvals.py

* Apply suggestions from code review

Co-authored-by: Maria Schuld <mariaschuld@gmail.com>

* update deprecation warning

* Update tests/ops/functions/test_eigvals.py

* update deprecation warning

* add another test

* suggested changes

* black

* black

* Apply suggestions from code review

Co-authored-by: David Wierichs <davidwierichs@gmail.com>

* changelog

* more

* bugfix

* suggested changes

* change parameter-frequency logic

* Apply suggestions from code review

Co-authored-by: Maria Schuld <mariaschuld@gmail.com>

* fix

Co-authored-by: Maria Schuld <mariaschuld@gmail.com>
Co-authored-by: David Wierichs <davidwierichs@gmail.com>

doc/introduction/operations.rst

@@ -44,7 +44,7 @@ and extracting information.
     ~pennylane.ctrl
     ~pennylane.matrix
     ~pennylane.eigvals
-
+    ~pennylane.generator
 
 All operator functions can be used on instantiated operators,
 

doc/releases/changelog-dev.md

@@ -12,6 +12,9 @@
   - `qml.eigvals()` for computing the eigenvalues of one or more operators.
     [(#2248)](https://github.com/PennyLaneAI/pennylane/pull/2248)
 
+  - `qml.generator()` for computing the generator of a single-parameter unitary operation.
+    [(#2256)](https://github.com/PennyLaneAI/pennylane/pull/2256)
+
   All operator transforms can be used on instantiated operators,
 
   ```pycon

pennylane/fourier/utils.py

@@ -18,7 +18,7 @@
 import numpy as np
 
 
-from pennylane.utils import get_generator
+import pennylane as qml
 
 
 def format_nvec(nvec):
@@ -63,8 +63,7 @@ def get_spectrum(op, decimals):
     Returns:
         set[float]: non-negative frequencies contributed by this input-encoding gate
     """
-    matrix, coeff = get_generator(op, return_matrix=True)
-    matrix = coeff * matrix
+    matrix = qml.matrix(qml.generator(op, format="observable"))
 
     # todo: use qml.math.linalg once it is tested properly
     evals = np.linalg.eigvalsh(matrix)

pennylane/operation.py

@@ -1291,23 +1291,15 @@ def parameter_frequencies(self):
         if self.num_params == 1:
             # if the operator has a single parameter, we can query the
             # generator, and if defined, use its eigenvalues.
-            gen = self.generator()
 
-            try:
-                gen_eigvals = tuple(self.generator().eigvals())
-                return qml.gradients.eigvals_to_frequencies(gen_eigvals)
-
-            except (MatrixUndefinedError, EigvalsUndefinedError):
-
-                if isinstance(gen, qml.Hamiltonian):
-                    mat = qml.utils.sparse_hamiltonian(gen).toarray()
-                    eigvals = tuple(np.round(np.linalg.eigvalsh(mat), 8))
-                    return qml.gradients.eigvals_to_frequencies(eigvals)
+            with warnings.catch_warnings():
+                warnings.filterwarnings(
+                    action="ignore", message=r".+ eigenvalues will be computed numerically\."
+                )
+                eigvals = qml.eigvals(qml.generator(self, format="observable"))
 
-                if isinstance(gen, qml.SparseHamiltonian):
-                    mat = gen.sparse_matrix().toarray()
-                    eigvals = tuple(np.round(np.linalg.eigvalsh(mat), 8))
-                    return qml.gradients.eigvals_to_frequencies(eigvals)
+            eigvals = tuple(np.round(eigvals, 8))
+            return qml.gradients.eigvals_to_frequencies(eigvals)
 
         raise OperatorPropertyUndefined(
             f"Operation {self.name} does not have parameter frequencies."
@@ -1398,14 +1390,13 @@ def __init__(self, *params, wires=None, do_queue=True, id=None):
         super().__init__(*params, wires=wires, do_queue=do_queue, id=id)
 
         # check the grad_recipe validity
-        if self.grad_method == "A":
-            if self.grad_recipe is None:
-                # default recipe for every parameter
-                self.grad_recipe = [None] * self.num_params
-            else:
-                assert (
-                    len(self.grad_recipe) == self.num_params
-                ), "Gradient recipe must have one entry for each parameter!"
+        if self.grad_recipe is None:
+            # default recipe for every parameter
+            self.grad_recipe = [None] * self.num_params
+        else:
+            assert (
+                len(self.grad_recipe) == self.num_params
+            ), "Gradient recipe must have one entry for each parameter!"
 
 
 class Channel(Operation, abc.ABC):
@@ -2394,8 +2385,8 @@ def operation_derivative(operation) -> np.ndarray:
         ValueError: if the operation does not have a generator or is not composed of a single
             trainable parameter
     """
-    generator, prefactor = qml.utils.get_generator(operation, return_matrix=True)
-    return 1j * prefactor * generator @ operation.get_matrix()
+    generator = qml.matrix(qml.generator(operation, format="observable"))
+    return 1j * generator @ operation.get_matrix()
 
 
 @qml.BooleanFn

pennylane/ops/functions/__init__.py

@@ -15,4 +15,5 @@
 This module contains functions that act on operators and tapes.
 """
 from .eigvals import eigvals
+from .generator import generator
 from .matrix import matrix

pennylane/ops/functions/generator.py

@@ -0,0 +1,180 @@
+# Copyright 2018-2021 Xanadu Quantum Technologies Inc.
+
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+
+#     http://www.apache.org/licenses/LICENSE-2.0
+
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+"""
+This module contains the qml.generator function.
+"""
+# pylint: disable=protected-access
+import pennylane as qml
+
+
+def _generator_observable(gen, op):
+    """Return the generator as type :class:`~.Hermitian`,
+    :class:`~.SparseHamiltonian`, or :class:`~.Hamiltonian`,
+    as provided by the original gate.
+    """
+    if isinstance(gen, (qml.Hermitian, qml.SparseHamiltonian)):
+        if not op.inverse:
+            return gen
+
+        param = gen.parameters[0]
+        wires = gen.wires
+
+        return gen.__class__(-param, wires=wires)
+
+    if op.inverse:
+        gen = -1.0 * gen
+
+    return gen
+
+
+def _generator_hamiltonian(gen, op):
+    """Return the generator as type :class:`~.Hamiltonian`."""
+    wires = op.wires
+
+    if isinstance(gen, qml.Hamiltonian):
+        H = gen
+
+    elif isinstance(gen, (qml.Hermitian, qml.SparseHamiltonian)):
+
+        if isinstance(gen, qml.Hermitian):
+            mat = gen.parameters[0]
+
+        elif isinstance(gen, qml.SparseHamiltonian):
+            mat = gen.parameters[0].toarray()
+
+        coeffs, obs = qml.utils.decompose_hamiltonian(mat, wire_order=wires, hide_identity=True)
+        H = qml.Hamiltonian(coeffs, obs)
+
+    elif isinstance(gen, qml.operation.Observable):
+        H = 1.0 * gen
+
+    if op.inverse:
+        H = -1.0 * H
+
+    return H
+
+
+def _generator_prefactor(gen, op):
+    r"""Return the generator as ```(obs, prefactor)`` representing
+    :math:`G=p \hat{O}`, where
+
+    - prefactor :math:`p` is a float
+    - observable `\hat{O}` is one of :class:`~.Hermitian`,
+      :class:`~.SparseHamiltonian`, or a tensor product
+      of Pauli words.
+    """
+    if isinstance(gen, (qml.Hermitian, qml.SparseHamiltonian)):
+        obs = gen
+        prefactor = 1.0
+
+    elif isinstance(gen, qml.operation.Observable):
+        # convert to a qml.Hamiltonian
+        gen = 1.0 * gen
+
+        if len(gen.ops) == 1:
+            # case where the Hamiltonian is a single Pauli word
+            obs = gen.ops[0]
+            prefactor = gen.coeffs[0]
+        else:
+            obs = gen
+            prefactor = 1.0
+
+    if op.inverse:
+        prefactor *= -1.0
+
+    return obs, prefactor
+
+
+@qml.op_transform
+def generator(op, format="prefactor"):
+    r"""Returns the generator of an operation.
+
+    Args:
+        op (.Operator or Callable): A single operator, or a function that
+            applies a single quantum operation.
+        format (str): The format to return the generator in. Must be one of ``'prefactor'``,
+            ``'observable'``, or ``'hamiltonian'``. See below for more details.
+
+    Returns:
+        .Observable or tuple[float, .Observable]: The returned generator, with format/type
+        dependent on the ``format`` argument.
+
+        * ``"prefactor"``: Return the generator as ```(obs, prefactor)`` (representing
+          :math:`G=p \hat{O}`), where
+
+          - observable `\hat{O}` is one of :class:`~.Hermitian`,
+            :class:`~.SparseHamiltonian`, or a tensor product
+            of Pauli words.
+          - prefactor :math:`p` is a float
+
+          The prefactor will in most cases be :math:`\pm 1.0`, unless the generator is a single Pauli
+          word, in which case the prefactor is the coefficient of the Pauli word.
+
+        * ``"observable"``: Return the generator as a single observable as directly defined
+          by ``op``. Returned generators may be any type of observable, including
+          :class:`~.Hermitian`, :class:`~.Tensor`,
+          :class:`~.SparseHamiltonian`, or :class:`~.Hamiltonian`.
+
+        * ``"hamiltonian"``: Similar to ``"observable"``, however the returned observable
+          will always be converted into :class:`~.Hamiltonian` regardless of how ``op``
+          encodes the generator.
+
+    **Example**
+
+    Given an operation, ``qml.generator`` returns the generator representation:
+
+    >>> op = qml.CRX(0.6, wires=[0, 1])
+    >>> qml.generator(op)
+    (Projector([1], wires=[0]) @ PauliX(wires=[1]), -0.5)
+
+    It can also be used in a functional form:
+
+    >>> qml.generator(qml.CRX)(0.6, wires=[0, 1])
+    (Projector([1], wires=[0]) @ PauliX(wires=[1]), -0.5)
+
+    By default, ``generator`` will return the generator in the format of ``(obs, prefactor)``,
+    corresponding to :math:`G=p \hat{O}`, where the observable :math:`\hat{O}` will
+    always be given in tensor product form, or as a dense/sparse matrix.
+
+    By using the ``format`` argument, the returned generator representation can
+    be altered:
+
+    >>> op = qml.RX(0.2, wires=0)
+    >>> qml.generator(op, format="prefactor")  # output will always be (prefactor, obs)
+    (Projector([1], wires=[0]), 1.0)
+    >>> qml.generator(op, format="hamiltonian")  # output will always be a Hamiltonian
+    <Hamiltonian: terms=1, wires=[0]>
+    >>> qml.generator(op, format="observable")  # ouput will be a simplified obs where possible
+    Projector([1], wires=[0])
+    """
+    if op.num_params != 1:
+        raise ValueError(f"Operation {op.name} is not written in terms of a single parameter")
+
+    gen = op.generator()
+
+    if not isinstance(gen, qml.operation.Observable):
+        raise qml.QuantumFunctionError(
+            f"Generator {gen.name} of operation {op.name} is not an observable"
+        )
+
+    if format == "prefactor":
+        return _generator_prefactor(gen, op)
+
+    if format == "hamiltonian":
+        return _generator_hamiltonian(gen, op)
+
+    if format == "observable":
+        return _generator_observable(gen, op)
+
+    raise ValueError("format must be one of ('prefactor', 'hamiltonian', 'observable')")

pennylane/tape/reversible.py

@@ -189,10 +189,10 @@ def reversible_diff(self, idx, params, **options):
 
         if op.name == "Rot":
             decomp = op.decomposition()
-            generator, multiplier = qml.utils.get_generator(decomp[p_idx])
+            generator, multiplier = qml.generator(decomp[p_idx])
             between_ops = decomp[p_idx + 1 :] + between_ops
         else:
-            generator, multiplier = qml.utils.get_generator(op)
+            generator, multiplier = qml.generator(op)
 
         # construct circuit to compute differentiated state
         between_ops_inverse = [copy.copy(op) for op in between_ops[::-1]]

pennylane/transforms/adjoint_metric_tensor.py

@@ -192,7 +192,8 @@ def _adjoint_metric_tensor_tape(tape, device):
     psi = _apply_operations(psi, group_after_trainable_op[-1], device)
 
     for j, outer_op in enumerate(trainable_operations):
-        generator_1, prefactor_1 = qml.utils.get_generator(outer_op, return_matrix=True)
+        generator_1, prefactor_1 = qml.generator(outer_op)
+        generator_1 = qml.matrix(generator_1)
 
         # the state vector phi is missing a factor of 1j * prefactor_1
         phi = device._apply_unitary(
@@ -223,7 +224,8 @@ def _adjoint_metric_tensor_tape(tape, device):
             lam = _apply_operations(lam, group_after_trainable_op[i], device, invert=True)
             inner_op = trainable_operations[i]
             # extract and apply G_i
-            generator_2, prefactor_2 = qml.utils.get_generator(inner_op, return_matrix=True)
+            generator_2, prefactor_2 = qml.generator(inner_op)
+            generator_2 = qml.matrix(generator_2)
             # this state vector is missing a factor of 1j * prefactor_2
             mu = device._apply_unitary(lam, qml.math.convert_like(generator_2, lam), inner_op.wires)
             phi_real = qml.math.reshape(qml.math.real(phi), (dim,))

pennylane/transforms/metric_tensor.py

@@ -390,7 +390,7 @@ def _metric_tensor_cov_matrix(tape, diag_approx):
 
         # for each operation in the layer, get the generator
         for op in curr_ops:
-            obs, s = qml.utils.get_generator(op)
+            obs, s = qml.generator(op)
             obs_list[-1].append(obs)
             coeffs_list[-1].append(s)
 
@@ -460,8 +460,8 @@ def _get_gen_op(op, allow_nonunitary, aux_wire):
 
     except KeyError as e:
         if allow_nonunitary:
-            gen, coeff = qml.utils.get_generator(op, return_matrix=True)
-            return qml.ControlledQubitUnitary(coeff * gen, control_wires=aux_wire, wires=op.wires)
+            mat = qml.matrix(qml.generator(op, format="observable"))
+            return qml.ControlledQubitUnitary(mat, control_wires=aux_wire, wires=op.wires)
 
         raise ValueError(
             f"Generator for operation {op} not known and non-unitary operations "

pennylane/transforms/op_transforms.py

@@ -264,9 +264,13 @@ def fn(self, obj, *args, **kwargs):
                 # the tape transform function if defined
                 return self.tape_fn(obj.expand(), *args, **kwargs)
 
-            except (AttributeError, OperationTransformError):
-                # if obj.expand() does not exist, or the tape transform
-                # function does not exist, simply raise the original exception
+            except (
+                AttributeError,
+                qml.operation.OperatorPropertyUndefined,
+                OperationTransformError,
+            ):
+                # if obj.expand() does not exist, a required operation property was not found,
+                # or the tape transform function does not exist, simply raise the original exception
                 raise e1 from None
 
     def tape_fn(self, obj, *args, **kwargs):
@@ -423,6 +427,12 @@ def wrapper(*args, **kwargs):
                 nonlocal wire_order
                 tape, verified_wire_order = self._make_tape(obj, wire_order, *args, **kwargs)
 
+                # HOTFIX: some operator transforms return a tape containing
+                # a single transformed operator. As a result, for now we need
+                # to treat a tape with a single operation as a single operation.
+                if len(getattr(tape, "operations", [])) == 1 and self._tape_fn is None:
+                    tape = tape.operations[0]
+
                 if wire_order is not None or (
                     "wire_order" in self._sig and isinstance(obj, qml.QNode)
                 ):