Source code for

# Copyright 2018-2023 Xanadu Quantum Technologies Inc.

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This file contains the definition of the dot function, which computes the dot product between
a vector and a list of operators.
# pylint: disable=too-many-branches
from collections import defaultdict
from typing import Callable, Sequence, Union

import pennylane as qml
from pennylane.operation import Operator, convert_to_opmath
from pennylane.pauli import PauliSentence, PauliWord
from pennylane.pulse import ParametrizedHamiltonian

[docs]def dot( coeffs: Sequence[Union[float, Callable]], ops: Sequence[Union[Operator, PauliWord, PauliSentence]], pauli=False, grouping_type=None, method="rlf", ) -> Union[Operator, ParametrizedHamiltonian, PauliSentence]: r"""Returns the dot product between the ``coeffs`` vector and the ``ops`` list of operators. This function returns the following linear combination: :math:`\sum_{k} c_k O_k`, where :math:`c_k` and :math:`O_k` are the elements inside the ``coeffs`` and ``ops`` arguments, respectively. Args: coeffs (Sequence[float, Callable]): sequence containing the coefficients of the linear combination ops (Sequence[Operator, PauliWord, PauliSentence]): sequence containing the operators of the linear combination. Can also be ``PauliWord`` or ``PauliSentence`` instances. pauli (bool, optional): If ``True``, a :class:`~.PauliSentence` operator is used to represent the linear combination. If False, a :class:`Sum` operator is returned. Defaults to ``False``. Note that when ``ops`` consists solely of ``PauliWord`` and ``PauliSentence`` instances, the function still returns a PennyLane operator when ``pauli=False``. grouping_type (str): The type of binary relation between Pauli words used to compute the grouping. Can be ``'qwc'``, ``'commuting'``, or ``'anticommuting'``. Note that if ``pauli=True``, the grouping will be ignored. method (str): The graph coloring heuristic to use in solving minimum clique cover for grouping, which can be ``'lf'`` (Largest First) or ``'rlf'`` (Recursive Largest First). This keyword argument is ignored if ``grouping_type`` is ``None``. Raises: ValueError: if the number of coefficients and operators does not match or if they are empty Returns: Operator or ParametrizedHamiltonian: operator describing the linear combination .. note:: If grouping is requested, the computed groupings are stored as a list of list of indices in ``Sum.grouping_indices``. The indices refer to the operators and coefficients returned by ``Sum.terms()``, not ``Sum.operands``, as these are not guaranteed to be equivalent. **Example** >>> coeffs = np.array([1.1, 2.2]) >>> ops = [qml.X(0), qml.Y(0)] >>>, ops) 1.1 * X(0) + 2.2 * Y(0) >>>, ops, pauli=True) 1.1 * X(0) + 2.2 * Y(0) Note that additions of the same operator are not executed by default. >>>[1., 1.], [qml.X(0), qml.X(0)]) X(0) + X(0) You can obtain a cleaner version by simplifying the resulting expression. >>>[1., 1.], [qml.X(0), qml.X(0)]).simplify() 2.0 * X(0) ``pauli=True`` can be used to construct a more efficient, simplified version of the operator. Note that it returns a :class:`~.PauliSentence`, which is not an :class:`~.Operator`. This specialized representation can be converted to an operator: >>>[1, 2], [qml.X(0), qml.X(0)], pauli=True).operation() 3.0 * X(0) Using ``pauli=True`` and then converting the result to an :class:`~.Operator` is much faster than using ``pauli=False``, but it only works for pauli words (see :func:`~.is_pauli_word`). If any of the parameters listed in ``coeffs`` are callables, the resulting dot product will be a :class:`~.ParametrizedHamiltonian`: >>> coeffs = [lambda p, t: p * jnp.sin(t) for _ in range(2)] >>> ops = [qml.X(0), qml.Y(0)] >>>, ops) ( <lambda>(params_0, t) * X(0) + <lambda>(params_1, t) * Y(0) ) .. details:: :title: Grouping Grouping information can be collected during construction using the ``grouping_type`` and ``method`` keyword arguments. For example: .. code-block:: python import pennylane as qml a = qml.X(0) b =, qml.X(1)) c = qml.Z(0) obs = [a, b, c] coeffs = [1.0, 2.0, 3.0] op =, obs, grouping_type="qwc") >>> op.grouping_indices ((2,), (0, 1)) ``grouping_type`` can be ``"qwc"`` (qubit-wise commuting), ``"commuting"``, or ``"anticommuting"``, and ``method`` can be ``"rlf"`` or ``"lf"``. To see more details about how these affect grouping, see :ref:`Pauli Graph Colouring<graph_colouring>` and :func:`~pennylane.pauli.group_observables`. """ for t in (Operator, PauliWord, PauliSentence): if isinstance(ops, t): raise ValueError( f"ops must be an Iterable of {t.__name__}'s, not a {t.__name__} itself." ) if len(coeffs) != len(ops): raise ValueError("Number of coefficients and operators does not match.") if len(coeffs) == 0 and len(ops) == 0: raise ValueError("Cannot compute the dot product of an empty sequence.") for t in (Operator, PauliWord, PauliSentence): if isinstance(ops, t): raise ValueError( f"ops must be an Iterable of {t.__name__}'s, not a {t.__name__} itself." ) if any(callable(c) for c in coeffs): return ParametrizedHamiltonian(coeffs, ops) # User-specified Pauli route if pauli: if all(isinstance(pauli, (PauliWord, PauliSentence)) for pauli in ops): # Use pauli arithmetic when ops are just PauliWord and PauliSentence instances return _dot_pure_paulis(coeffs, ops) # Else, transform all ops to pauli sentences return _dot_with_ops_and_paulis(coeffs, ops) # Convert possible PauliWord and PauliSentence instances to operation ops = [op.operation() if isinstance(op, (PauliWord, PauliSentence)) else op for op in ops] # When casting a Hamiltonian to a Sum, we also cast its inner Tensors to Prods ops = (convert_to_opmath(op) for op in ops) operands = [op if coeff == 1 else qml.s_prod(coeff, op) for coeff, op in zip(coeffs, ops)] return ( operands[0] if len(operands) == 1 else qml.sum(*operands, grouping_type=grouping_type, method=method) )
def _dot_with_ops_and_paulis(coeffs: Sequence[float], ops: Sequence[Operator]): """Compute dot when operators are a mix of pennylane operators, PauliWord and PauliSentence by turning them all into a PauliSentence instance. Returns a PauliSentence instance""" pauli_words = defaultdict(lambda: 0) for coeff, op in zip(coeffs, ops): sentence = qml.pauli.pauli_sentence(op) for pw in sentence: pauli_words[pw] += sentence[pw] * coeff return qml.pauli.PauliSentence(pauli_words) def _dot_pure_paulis(coeffs: Sequence[float], ops: Sequence[Union[PauliWord, PauliSentence]]): """Faster computation of dot when all ops are PauliSentences or PauliWords""" return sum((c * op for c, op in zip(coeffs[1:], ops[1:])), start=coeffs[0] * ops[0])