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# Source code for qiskit.algorithms.optimizers.nft

```# This code is part of Qiskit.
#
# (C) Copyright IBM 2019, 2020.
#
# obtain a copy of this license in the LICENSE.txt file in the root directory
#
# 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.

"""Nakanishi-Fujii-Todo algorithm."""

from typing import Optional

import numpy as np
from scipy.optimize import OptimizeResult

from .scipy_optimizer import SciPyOptimizer

[docs]class NFT(SciPyOptimizer):
"""
Nakanishi-Fujii-Todo algorithm.

See https://arxiv.org/abs/1903.12166
"""

_OPTIONS = ["maxiter", "maxfev", "disp", "reset_interval"]

# pylint: disable=unused-argument
def __init__(
self,
maxiter: Optional[int] = None,
maxfev: int = 1024,
disp: bool = False,
reset_interval: int = 32,
options: Optional[dict] = None,
**kwargs,
) -> None:
"""
Built out using scipy framework, for details, please refer to
https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html.

Args:
maxiter: Maximum number of iterations to perform.
maxfev: Maximum number of function evaluations to perform.
disp: disp
reset_interval: The minimum estimates directly once
in ``reset_interval`` times.
options: A dictionary of solver options.

Notes:
In this optimization method, the optimization function have to satisfy
three conditions written in [1]_.

References:
.. [1] K. M. Nakanishi, K. Fujii, and S. Todo. 2019.
Sequential minimal optimization for quantum-classical hybrid algorithms.
arXiv preprint arXiv:1903.12166.
"""
if options is None:
options = {}
for k, v in list(locals().items()):
if k in self._OPTIONS:
options[k] = v
super().__init__(method=nakanishi_fujii_todo, options=options, **kwargs)

# pylint: disable=invalid-name
def nakanishi_fujii_todo(
fun, x0, args=(), maxiter=None, maxfev=1024, reset_interval=32, eps=1e-32, callback=None, **_
):
"""
Find the global minimum of a function using the nakanishi_fujii_todo
algorithm [1].
Args:
fun (callable): ``f(x, *args)``
Function to be optimized.  ``args`` can be passed as an optional item
in the dict ``minimizer_kwargs``.
This function must satisfy the three condition written in Ref. [1].
x0 (ndarray): shape (n,)
Initial guess. Array of real elements of size (n,),
where 'n' is the number of independent variables.
args (tuple, optional):
Extra arguments passed to the objective function.
maxiter (int):
Maximum number of iterations to perform.
Default: None.
maxfev (int):
Maximum number of function evaluations to perform.
Default: 1024.
reset_interval (int):
The minimum estimates directly once in ``reset_interval`` times.
Default: 32.
eps (float): eps
callback (callable, optional):
Called after each iteration.
Returns:
OptimizeResult:
The optimization result represented as a ``OptimizeResult`` object.
Important attributes are: ``x`` the solution array. See
`OptimizeResult` for a description of other attributes.
Notes:
In this optimization method, the optimization function have to satisfy
three conditions written in [1].
References:
.. [1] K. M. Nakanishi, K. Fujii, and S. Todo. 2019.
Sequential minimal optimization for quantum-classical hybrid algorithms.
arXiv preprint arXiv:1903.12166.
"""

x0 = np.asarray(x0)
recycle_z0 = None
niter = 0
funcalls = 0

while True:

idx = niter % x0.size

if reset_interval > 0:
if niter % reset_interval == 0:
recycle_z0 = None

if recycle_z0 is None:
z0 = fun(np.copy(x0), *args)
funcalls += 1
else:
z0 = recycle_z0

p = np.copy(x0)
p[idx] = x0[idx] + np.pi / 2
z1 = fun(p, *args)
funcalls += 1

p = np.copy(x0)
p[idx] = x0[idx] - np.pi / 2
z3 = fun(p, *args)
funcalls += 1

z2 = z1 + z3 - z0
c = (z1 + z3) / 2
a = np.sqrt((z0 - z2) ** 2 + (z1 - z3) ** 2) / 2
b = np.arctan((z1 - z3) / ((z0 - z2) + eps * (z0 == z2))) + x0[idx]
b += 0.5 * np.pi + 0.5 * np.pi * np.sign((z0 - z2) + eps * (z0 == z2))

x0[idx] = b
recycle_z0 = c - a

niter += 1

if callback is not None:
callback(np.copy(x0))

if maxfev is not None:
if funcalls >= maxfev:
break

if maxiter is not None:
if niter >= maxiter:
break

return OptimizeResult(
fun=fun(np.copy(x0), *args), x=x0, nit=niter, nfev=funcalls, success=(niter > 1)
)
```