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.
from collections import defaultdict
from typing import Sequence, Union, Callable

import pennylane as qml
from pennylane.operation import Operator, Tensor
from pennylane.pulse import ParametrizedHamiltonian

[docs]def dot( coeffs: Sequence[Union[float, Callable]], ops: Sequence[Operator], pauli=False ) -> Union[Operator, ParametrizedHamiltonian]: 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]): sequence containing the operators of the linear combination 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``. 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 **Example** >>> coeffs = np.array([1.1, 2.2]) >>> ops = [qml.PauliX(0), qml.PauliY(0)] >>>, ops) (1.1*(PauliX(wires=[0]))) + (2.2*(PauliY(wires=[0]))) >>>, ops, pauli=True) 1.1 * X(0) + 2.2 * Y(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.PauliX(0), qml.PauliX(0)], pauli=True).operation() 3.0*(PauliX(wires=[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.PauliX(0), qml.PauliY(0)] >>>, ops) (<lambda>(params_0, t)*(PauliX(wires=[0]))) + (<lambda>(params_1, t)*(PauliY(wires=[0]))) """ 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.") if any(callable(c) for c in coeffs): return ParametrizedHamiltonian(coeffs, ops) if pauli: return _pauli_dot(coeffs, ops) # When casting a Hamiltonian to a Sum, we also cast its inner Tensors to Prods ops = [*op.obs) if isinstance(op, Tensor) else op for op in ops] if coeffs[0] != 1 and qml.math.allequal(coeffs[0], coeffs): # Coefficients have the same value (different to 1) return qml.s_prod(coeffs[0], ops[0] if len(ops) == 1 else qml.sum(*ops)) abs_coeffs = qml.math.abs(coeffs) if abs_coeffs[0] != 1 and qml.math.allequal(abs_coeffs[0], abs_coeffs): # Coefficients have the same absolute value (different to 1) gcd = abs(coeffs[0]) coeffs = [c / gcd for c in coeffs] return qml.s_prod(gcd,, 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)
def _pauli_dot(coeffs: Sequence[float], ops: Sequence[Operator]): 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)