Source code for pennylane.ops.op_math.sprod

# Copyright 2018-2022 Xanadu Quantum Technologies Inc.

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This file contains the implementation of the SProd class which contains logic for
computing the scalar product of operations.
from typing import Union
from copy import copy

import pennylane as qml
import pennylane.math as qnp
from pennylane.operation import Operator
from pennylane.ops.op_math.pow import Pow
from pennylane.ops.op_math.sum import Sum
from pennylane.queuing import QueuingManager

from .symbolicop import ScalarSymbolicOp

[docs]def s_prod(scalar, operator, lazy=True, id=None): r"""Construct an operator which is the scalar product of the given scalar and operator provided. Args: scalar (float or complex): the scale factor being multiplied to the operator. operator (~.operation.Operator): the operator which will get scaled. Keyword Args: lazy=True (bool): If ``lazy=False`` and the operator is already a scalar product operator, the scalar provided will simply be combined with the existing scaling factor. id (str or None): id for the scalar product operator. Default is None. Returns: ~ops.op_math.SProd: The operator representing the scalar product. .. note:: This operator supports a batched base, a batched coefficient and a combination of both: >>> op = qml.s_prod(scalar=4, operator=qml.RX([1, 2, 3], wires=0)) >>> qml.matrix(op).shape (3, 2, 2) >>> op = qml.s_prod(scalar=[1, 2, 3], operator=qml.RX(1, wires=0)) >>> qml.matrix(op).shape (3, 2, 2) >>> op = qml.s_prod(scalar=[4, 5, 6], operator=qml.RX([1, 2, 3], wires=0)) >>> qml.matrix(op).shape (3, 2, 2) But it doesn't support batching of operators: >>> op = qml.s_prod(scalar=4, operator=[qml.RX(1, wires=0), qml.RX(2, wires=0)]) AttributeError: 'list' object has no attribute 'batch_size' .. seealso:: :class:`~.ops.op_math.SProd` and :class:`~.ops.op_math.SymbolicOp` **Example** >>> sprod_op = s_prod(2.0, qml.PauliX(0)) >>> sprod_op 2.0*(PauliX(wires=[0])) >>> sprod_op.matrix() array([[ 0., 2.], [ 2., 0.]]) """ if lazy or not isinstance(operator, SProd): return SProd(scalar, operator, id=id) sprod_op = SProd(scalar=scalar * operator.scalar, base=operator.base, id=id) QueuingManager.remove(operator) return sprod_op
[docs]class SProd(ScalarSymbolicOp): r"""Arithmetic operator representing the scalar product of an operator with the given scalar. Args: scalar (float or complex): the scale factor being multiplied to the operator. base (~.operation.Operator): the operator which will get scaled. Keyword Args: id (str or None): id for the scalar product operator. Default is None. .. note:: Currently this operator can not be queued in a circuit as an operation, only measured terminally. .. seealso:: :func:`~.ops.op_math.s_prod` **Example** >>> sprod_op = SProd(1.23, qml.PauliX(0)) >>> sprod_op 1.23*(PauliX(wires=[0])) >>> qml.matrix(sprod_op) array([[0. , 1.23], [1.23, 0. ]]) >>> sprod_op.terms() ([1.23], [PauliX(wires=[0]]) .. details:: :title: Usage Details The SProd operation can also be measured inside a qnode as an observable. If the circuit is parameterized, then we can also differentiate through the observable. .. code-block:: python dev = qml.device("default.qubit", wires=1) @qml.qnode(dev, diff_method="best") def circuit(scalar, theta): qml.RX(theta, wires=0) return qml.expval(qml.s_prod(scalar, qml.Hadamard(wires=0))) >>> scalar, theta = (1.2, 3.4) >>> qml.grad(circuit, argnum=[0,1])(scalar, theta) (array(-0.68362956), array(0.21683382)) """ _name = "SProd" def _flatten(self): return (self.scalar, self.base), tuple() @classmethod def _unflatten(cls, data, _): return cls(data[0], data[1]) def __init__(self, scalar: Union[int, float, complex], base: Operator, id=None): super().__init__(base=base, scalar=scalar, id=id) if (base_pauli_rep := getattr(self.base, "_pauli_rep", None)) and (self.batch_size is None): scalar = copy(self.scalar) if qnp.get_interface(scalar) == "tensorflow" and not scalar.dtype.is_complex: scalar = qnp.cast(scalar, "complex128") pr = {pw:, scalar) for pw, coeff in base_pauli_rep.items()} self._pauli_rep = qml.pauli.PauliSentence(pr) else: self._pauli_rep = None def __repr__(self): """Constructor-call-like representation.""" return f"{self.scalar}*({self.base})"
[docs] def label(self, decimals=None, base_label=None, cache=None): """The label produced for the SProd op.""" scalar_val = ( f"{self.scalar}" if decimals is None else format(qml.math.toarray(self.scalar), f".{decimals}f") ) return base_label or f"{scalar_val}*{self.base.label(decimals=decimals, cache=cache)}"
@property def num_params(self): """Number of trainable parameters that the operator depends on. Usually 1 + the number of trainable parameters for the base op. Returns: int: number of trainable parameters """ return 1 + self.base.num_params
[docs] def terms(self): # is this method necessary for this class? r"""Representation of the operator as a linear combination of other operators. .. math:: O = \sum_i c_i O_i A ``TermsUndefinedError`` is raised if no representation by terms is defined. Returns: tuple[list[tensor_like or float], list[.Operation]]: list of coefficients :math:`c_i` and list of operations :math:`O_i` """ return [self.scalar], [self.base]
@property def is_hermitian(self): """If the base operator is hermitian and the scalar is real, then the scalar product operator is hermitian.""" return self.base.is_hermitian and not qml.math.iscomplex(self.scalar) # pylint: disable=arguments-renamed,invalid-overridden-method @property def has_diagonalizing_gates(self): """Bool: Whether the Operator returns defined diagonalizing gates.""" return self.base.has_diagonalizing_gates
[docs] def diagonalizing_gates(self): r"""Sequence of gates that diagonalize the operator in the computational basis. Given the eigendecomposition :math:`O = U \Sigma U^{\dagger}` where :math:`\Sigma` is a diagonal matrix containing the eigenvalues, the sequence of diagonalizing gates implements the unitary :math:`U^{\dagger}`. The diagonalizing gates rotate the state into the eigenbasis of the operator. A ``DiagGatesUndefinedError`` is raised if no representation by decomposition is defined. .. seealso:: :meth:`~.Operator.compute_diagonalizing_gates`. Returns: list[.Operator] or None: a list of operators """ return self.base.diagonalizing_gates()
[docs] def eigvals(self): r"""Return the eigenvalues of the specified operator. This method uses pre-stored eigenvalues for standard observables where possible and stores the corresponding eigenvectors from the eigendecomposition. Returns: array: array containing the eigenvalues of the operator. """ base_eigs = self.base.eigvals() if qml.math.get_interface(self.scalar) == "torch" and self.scalar.requires_grad: base_eigs = qml.math.convert_like(base_eigs, self.scalar) return self.scalar * base_eigs
[docs] def sparse_matrix(self, wire_order=None): """Computes, by default, a `scipy.sparse.csr_matrix` representation of this Tensor. This is useful for larger qubit numbers, where the dense matrix becomes very large, while consisting mostly of zero entries. Args: wire_order (Iterable): Wire labels that indicate the order of wires according to which the matrix is constructed. If not provided, ``self.wires`` is used. Returns: :class:`scipy.sparse._csr.csr_matrix`: sparse matrix representation """ if self._pauli_rep: # Get the sparse matrix from the PauliSentence representation return self._pauli_rep.to_mat(wire_order=wire_order or self.wires, format="csr") mat = self.base.sparse_matrix(wire_order=wire_order).multiply(self.scalar) mat.eliminate_zeros() return mat
@property def has_matrix(self): """Bool: Whether or not the Operator returns a defined matrix.""" return isinstance(self.base, qml.Hamiltonian) or self.base.has_matrix @staticmethod def _matrix(scalar, mat): return scalar * mat @property def _queue_category(self): # don't queue scalar prods as they might not be Unitary! """Used for sorting objects into their respective lists in `QuantumTape` objects. This property is a temporary solution that should not exist long-term and should not be used outside of ``QuantumTape._process_queue``. Returns: None """ return None
[docs] def pow(self, z): """Returns the operator raised to a given power.""" return [SProd(scalar=self.scalar**z, base=Pow(base=self.base, z=z))]
[docs] def adjoint(self): """Create an operation that is the adjoint of this one. Adjointed operations are the conjugated and transposed version of the original operation. Adjointed ops are equivalent to the inverted operation for unitary gates. Returns: The adjointed operation. """ return SProd(scalar=qml.math.conjugate(self.scalar), base=qml.adjoint(self.base))
# pylint: disable=too-many-return-statements
[docs] def simplify(self) -> Operator: """Reduce the depth of nested operators to the minimum. Returns: .Operator: simplified operator """ # try using pauli_rep: if pr := self._pauli_rep: pr.simplify() return pr.operation(wire_order=self.wires) if self.scalar == 1: return self.base.simplify() if isinstance(self.base, SProd): scalar = self.scalar * self.base.scalar if scalar == 1: return self.base.base.simplify() return SProd(scalar=scalar, base=self.base.base.simplify()) new_base = self.base.simplify() if isinstance(new_base, Sum): return Sum( *(SProd(scalar=self.scalar, base=summand).simplify() for summand in new_base) ) if isinstance(new_base, SProd): return SProd(scalar=self.scalar, base=new_base).simplify() return SProd(scalar=self.scalar, base=new_base)