# -*- coding: utf-8 -*-
# This code is part of Qiskit.
#
# (C) Copyright IBM 2020.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""
QDrift Class
"""
import numpy as np
from .trotterization_base import TrotterizationBase
from ...operator_base import OperatorBase
from ...list_ops.summed_op import SummedOp
from ...list_ops.composed_op import ComposedOp
# pylint: disable=invalid-name
[docs]class QDrift(TrotterizationBase):
""" The QDrift Trotterization method, which selects each each term in the
Trotterization randomly, with a probability proportional to its weight. Based on the work
of Earl Campbell in https://arxiv.org/abs/1811.08017.
"""
def __init__(self, reps: int = 1) -> None:
r"""
Args:
reps: The number of times to repeat the Trotterization circuit.
"""
super().__init__(reps=reps)
[docs] def convert(self, operator: OperatorBase) -> OperatorBase:
if not isinstance(operator, SummedOp):
raise TypeError('Trotterization converters can only convert SummedOps.')
# We artificially make the weights positive, TODO check approximation performance
weights = np.abs([op.coeff for op in operator.oplist])
lambd = sum(weights)
N = 2 * (lambd ** 2) * (operator.coeff ** 2)
factor = lambd * operator.coeff / (N * self.reps)
# The protocol calls for the removal of the individual coefficients,
# and multiplication by a constant factor.
scaled_ops = [(op * (factor / op.coeff)).exp_i() for op in operator.oplist]
sampled_ops = np.random.choice(scaled_ops, size=(int(N * self.reps),), p=weights / lambd)
return ComposedOp(sampled_ops).reduce()