Source code for pennylane.ops.op_math.evolution

# Copyright 2018-2023 Xanadu Quantum Technologies Inc.

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"""
This submodule defines the Evolution class.
"""
from copy import copy
from warnings import warn

import pennylane as qml
from pennylane import math
from pennylane.operation import GeneratorUndefinedError

from .exp import Exp


[docs]class Evolution(Exp): r"""Create an exponential operator that defines a generator, of the form :math:`e^{-ix\hat{G}}` Args: base (~.operation.Operator): The operator to be used as a generator, G. param (float): The evolution parameter, x. This parameter is expected not to have any complex component. num_steps (int): The number of steps used in the decomposition of the exponential operator, also known as the Trotter number. If this value is `None` and the Suzuki-Trotter decomposition is needed, an error will be raised. id (str): id for the Evolution operator. Default is None. Returns: :class:`Evolution`: A :class:`~.operation.Operator` representing an operator exponential of the form :math:`e^{-ix\hat{G}}`, where x is real. **Usage Details** In contrast to the general :class:`~.Exp` class, the ``Evolution`` operator :math:`e^{-ix\hat{G}}` is constrained to have a single trainable parameter, x. Any parameters contained in the base operator are not trainable. This allows the operator to be differentiated with regard to the evolution parameter. Defining a mathematically identical operator using the :class:`~.Exp` class will be incompatible with a variety of PennyLane functions that require only a single trainable parameter. **Example** This symbolic operator can be used to make general rotation operators: >>> theta = np.array(1.23) >>> op = Evolution(qml.X(0), 0.5 * theta) >>> qml.math.allclose(op.matrix(), qml.RX(theta, wires=0).matrix()) True Or to define a time evolution operator for a time-independent Hamiltonian: >>> H = qml.Hamiltonian([1, 1], [qml.Y(0), qml.X(1)]) >>> t = 10e-6 >>> U = Evolution(H, t) If the base operator is Hermitian, then the gate can be used in a circuit, though it may not be supported by the device and may not be differentiable. >>> @qml.qnode(qml.device('default.qubit', wires=1)) ... def circuit(x): ... qml.ops.Evolution(qml.X(0), 0.5 * x) ... return qml.expval(qml.Z(0)) >>> print(qml.draw(circuit)(1.23)) 0: ──Exp(-0.61j X)─┤ <Z> """ _name = "Evolution" num_params = 1 # pylint: disable=too-many-arguments def __init__(self, generator, param=1, num_steps=None, id=None): super().__init__(generator, coeff=-1j * param, num_steps=num_steps, id=id) self._data = (param,) def __repr__(self): return ( f"Evolution({self.coeff} {self.base})" if self.base.arithmetic_depth > 0 else f"Evolution({self.coeff} {self.base.name})" ) @property def data(self): return self._data @data.setter def data(self, new_data): self._data = new_data @property def param(self): """A real coefficient with ``1j`` factored out.""" return self.data[0] @property def coeff(self): return -1j * self.data[0]
[docs] def label(self, decimals=None, base_label=None, cache=None): param = ( -self.data[0] if decimals is None else format(math.toarray(-self.data[0]), f".{decimals}f") ) return base_label or f"Exp({param}j {self.base.label(decimals=decimals, cache=cache)})"
[docs] def simplify(self): new_base = self.base.simplify() if isinstance(new_base, qml.ops.op_math.SProd): # pylint: disable=no-member return Evolution(new_base.base, self.param * new_base.scalar) return Evolution(new_base, self.param)
# pylint: disable=arguments-renamed, invalid-overridden-method @property def has_generator(self): return not qml.math.real(self.coeff)
[docs] def generator(self): r"""Generator of an operator that is in single-parameter-form. For example, for operator .. math:: U(\phi) = e^{-i\phi (0.5 Y + Z\otimes X)} we get the generator >>> U.generator() (0.5) [Y0] + (1.0) [Z0 X1] """ if not self.base.is_hermitian: warn(f"The base {self.base} may not be hermitian.") if qml.math.real(self.coeff): raise GeneratorUndefinedError( f"The operator coefficient {self.coeff} is not imaginary; the expected format is exp(-ixG)." f"The generator is not defined." ) return self.base
def __copy__(self): copied = super().__copy__() copied._data = copy(self._data) return copied