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Release 1.1.0
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7 changes: 5 additions & 2 deletions HISTORY.rst
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=======


(next release)
--------------
1.1.0 (2020-03-24)
------------------

* Added: Support for Python 3.8
* Added: Support for QuTiP 4.5.0
* Added: Support for parallelization with loky_ (`#72`_)
* Added: ``krotov.parallelization.set_parallelization`` function
* Added: ``krotov.parallelization.parallel_map`` function (improved implementation of QuTiP's ``parallel_map``)
* Added: Ability to use threadpoolctl_ to limit unwanted threading
* Added: `limit_thread_pool` option to ``krotov.optimize_pulses``
* Changed: ``krotov.propagators.expm`` now guarantees single-threaded execution

Expand Down Expand Up @@ -101,6 +103,7 @@ History
.. _loky: https://loky.readthedocs.io/
.. _gh-pages: https://qucontrol.github.io/krotov
.. _Doctr: https://drdoctr.github.io
.. _threadpoolctl: https://github.com/joblib/threadpoolctl
.. _@uiofgh: https://github.com/uiofgh
.. _@TejasAvinashShetty: https://github.com/TejasAvinashShetty
.. _@timohillmann: https://github.com/timohillmann
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10 changes: 5 additions & 5 deletions README.rst
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Expand Up @@ -27,7 +27,7 @@ Krotov Python Package
:target: https://opensource.org/licenses/BSD-3-Clause
.. image:: https://mybinder.org/badge_logo.svg
:alt: Launch Binder
:target: https://mybinder.org/v2/gh/qucontrol/krotov/v1.0.0?filepath=docs%2Fnotebooks
:target: https://mybinder.org/v2/gh/qucontrol/krotov/v1.1.0?filepath=docs%2Fnotebooks
.. image:: https://img.shields.io/badge/DOI-10.21468/SciPostPhys.7.6.080-blue.svg
:alt: DOI
:target: https://doi.org/10.21468/SciPostPhys.7.6.080
Expand All @@ -43,7 +43,7 @@ Development happens on `Github`_. You can read the full documentation `online`__
.. _Documentation: https://qucontrol.github.io/krotov
__ Documentation_

If you use the ``krotov`` package in your research, please `cite it <https://qucontrol.github.io/krotov/v1.0.0/01_overview.html#citing-the-krotov-package>`_.
If you use the ``krotov`` package in your research, please `cite it <https://qucontrol.github.io/krotov/v1.1.0/01_overview.html#citing-the-krotov-package>`_.

.. _QDYN Fortran library: https://www.qdyn-library.net
.. _QuTiP: http://qutip.org
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number of control fields over all the objectives.

.. |krotov.Objective| replace:: ``krotov.Objective``
.. _krotov.Objective: https://qucontrol.github.io/krotov/v1.0.0/API/krotov.objectives.html#krotov.objectives.Objective
.. _krotov.Objective: https://qucontrol.github.io/krotov/v1.1.0/API/krotov.objectives.html#krotov.objectives.Objective

.. |krotov.optimize_pulses| replace:: ``krotov.optimize_pulses``
.. _krotov.optimize_pulses: https://qucontrol.github.io/krotov/v1.0.0/API/krotov.optimize.html#krotov.optimize.optimize_pulses
.. _krotov.optimize_pulses: https://qucontrol.github.io/krotov/v1.1.0/API/krotov.optimize.html#krotov.optimize.optimize_pulses

See `Using Krotov with QuTiP <https://qucontrol.github.io/krotov/v1.0.0/08_qutip_usage.html#using-krotov-with-qutip>`_ and `Examples <https://qucontrol.github.io/krotov/v1.0.0/09_examples.html>`_ for details.
See `Using Krotov with QuTiP <https://qucontrol.github.io/krotov/v1.1.0/08_qutip_usage.html#using-krotov-with-qutip>`_ and `Examples <https://qucontrol.github.io/krotov/v1.1.0/09_examples.html>`_ for details.

.. _Jupyter notebook: https://jupyter.org
2 changes: 1 addition & 1 deletion binder/environment.yml
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Expand Up @@ -8,4 +8,4 @@ dependencies:
- pip:
- matplotlib
- watermark
- git+https://github.com/qucontrol/krotov.git@master#egg=krotov
- krotov==1.1.0
2 changes: 1 addition & 1 deletion docs/09_examples.rst
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.. raw:: html

<a href="http://nbviewer.jupyter.org/github/qucontrol/krotov/blob/master/docs/notebooks" target="_blank"><img alt="Render on nbviewer" src="https://img.shields.io/badge/render%20on-nbviewer-orange.svg" style="vertical-align:text-bottom"></a>&nbsp;<a href="https://mybinder.org/v2/gh/qucontrol/krotov/master?filepath=docs%2Fnotebooks" target="_blank"><img alt="Launch Binder" src="https://mybinder.org/badge_logo.svg" style="vertical-align:text-bottom"></a>
<a href="http://nbviewer.jupyter.org/github/qucontrol/krotov/blob/v1.1.0/docs/notebooks" target="_blank"><img alt="Render on nbviewer" src="https://img.shields.io/badge/render%20on-nbviewer-orange.svg" style="vertical-align:text-bottom"></a>&nbsp;<a href="https://mybinder.org/v2/gh/qucontrol/krotov/v1.1.0?filepath=docs%2Fnotebooks" target="_blank"><img alt="Launch Binder" src="https://mybinder.org/badge_logo.svg" style="vertical-align:text-bottom"></a>

.. toctree::
:maxdepth: 1
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8 changes: 4 additions & 4 deletions docs/_README.patch
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Expand Up @@ -12,7 +12,7 @@
.. _Documentation: https://qucontrol.github.io/krotov
__ Documentation_

-If you use the ``krotov`` package in your research, please `cite it <https://qucontrol.github.io/krotov/v1.0.0/01_overview.html#citing-the-krotov-package>`_.
-If you use the ``krotov`` package in your research, please `cite it <https://qucontrol.github.io/krotov/v1.1.0/01_overview.html#citing-the-krotov-package>`_.
+If you use the :mod:`krotov` package in your research, please :ref:`cite it <CitingKrotov>`.

.. _QDYN Fortran library: https://www.qdyn-library.net
Expand Down Expand Up @@ -55,12 +55,12 @@
number of control fields over all the objectives.

-.. |krotov.Objective| replace:: ``krotov.Objective``
-.. _krotov.Objective: https://qucontrol.github.io/krotov/v1.0.0/API/krotov.objectives.html#krotov.objectives.Objective
-.. _krotov.Objective: https://qucontrol.github.io/krotov/v1.1.0/API/krotov.objectives.html#krotov.objectives.Objective

-.. |krotov.optimize_pulses| replace:: ``krotov.optimize_pulses``
-.. _krotov.optimize_pulses: https://qucontrol.github.io/krotov/v1.0.0/API/krotov.optimize.html#krotov.optimize.optimize_pulses
-.. _krotov.optimize_pulses: https://qucontrol.github.io/krotov/v1.1.0/API/krotov.optimize.html#krotov.optimize.optimize_pulses
-
-See `Using Krotov with QuTiP <https://qucontrol.github.io/krotov/v1.0.0/08_qutip_usage.html#using-krotov-with-qutip>`_ and `Examples <https://qucontrol.github.io/krotov/v1.0.0/09_examples.html>`_ for details.
-See `Using Krotov with QuTiP <https://qucontrol.github.io/krotov/v1.1.0/08_qutip_usage.html#using-krotov-with-qutip>`_ and `Examples <https://qucontrol.github.io/krotov/v1.1.0/09_examples.html>`_ for details.
+See :ref:`using-krotov-with-qutip` and :ref:`krotov-example-notebooks` for details.

.. _Jupyter notebook: https://jupyter.org
1 change: 1 addition & 0 deletions docs/build_pdf.py
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Expand Up @@ -42,6 +42,7 @@ def _patch_line(line):
r'\sphinxurl{krotov\_pseudocode.pdf}',
r'\url{https://qucontrol.github.io/krotov/master/krotov_pseudocode.pdf}',
)
line = line.replace(r'\sphinxhyphen{}', '-')
if line.startswith(r'\(\newcommand'):
return None
if line == r'\begin{split}\begin{equation}' + "\n":
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2 changes: 1 addition & 1 deletion docs/index.rst
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Expand Up @@ -27,7 +27,7 @@ Welcome to the Krotov package's documentation!
:target: https://opensource.org/licenses/BSD-3-Clause
.. image:: https://mybinder.org/badge_logo.svg
:alt: Launch Binder
:target: https://mybinder.org/v2/gh/qucontrol/krotov/v1.0.0?filepath=docs%2Fnotebooks
:target: https://mybinder.org/v2/gh/qucontrol/krotov/v1.1.0?filepath=docs%2Fnotebooks
.. image:: https://img.shields.io/badge/DOI-10.21468/SciPostPhys.7.6.080-blue.svg
:alt: DOI
:target: https://doi.org/10.21468/SciPostPhys.7.6.080
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50 changes: 25 additions & 25 deletions docs/notebooks/01_example_simple_state_to_state.ipynb
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"name": "stdout",
"output_type": "stream",
"text": [
"scipy 1.3.1\n",
"numpy 1.17.2\n",
"qutip 4.5.0\n",
"matplotlib 3.2.1\n",
"krotov 1.0.0+dev\n",
"qutip 4.4.1\n",
"scipy 1.3.1\n",
"krotov 1.1.0\n",
"matplotlib.pylab 1.17.2\n",
"numpy 1.17.2\n",
"CPython 3.7.6\n",
"IPython 7.13.0\n"
]
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"output_type": "stream",
"text": [
"iter. J_T ∫gₐ(t)dt J ΔJ_T ΔJ secs\n",
"0 9.51e-01 0.00e+00 9.51e-01 n/a n/a 0\n",
"1 9.24e-01 2.32e-03 9.27e-01 -2.70e-02 -2.47e-02 1\n",
"2 8.83e-01 3.53e-03 8.87e-01 -4.11e-02 -3.75e-02 1\n",
"3 8.23e-01 5.22e-03 8.28e-01 -6.06e-02 -5.54e-02 1\n",
"4 7.38e-01 7.39e-03 7.45e-01 -8.52e-02 -7.78e-02 1\n",
"5 6.26e-01 9.75e-03 6.36e-01 -1.11e-01 -1.01e-01 1\n",
"6 4.96e-01 1.16e-02 5.07e-01 -1.31e-01 -1.19e-01 1\n",
"7 3.62e-01 1.21e-02 3.74e-01 -1.34e-01 -1.22e-01 1\n",
"8 2.44e-01 1.09e-02 2.55e-01 -1.18e-01 -1.07e-01 1\n",
"9 1.53e-01 8.43e-03 1.62e-01 -9.03e-02 -8.19e-02 1\n",
"10 9.20e-02 5.80e-03 9.78e-02 -6.14e-02 -5.56e-02 1\n",
"11 5.35e-02 3.66e-03 5.72e-02 -3.85e-02 -3.48e-02 1\n",
"12 3.06e-02 2.19e-03 3.28e-02 -2.29e-02 -2.07e-02 1\n",
"13 1.73e-02 1.27e-03 1.86e-02 -1.33e-02 -1.20e-02 1\n",
"14 9.79e-03 7.24e-04 1.05e-02 -7.55e-03 -6.82e-03 1\n",
"15 5.52e-03 4.10e-04 5.93e-03 -4.27e-03 -3.86e-03 1\n",
"16 3.11e-03 2.31e-04 3.35e-03 -2.41e-03 -2.18e-03 1\n",
"17 1.76e-03 1.30e-04 1.89e-03 -1.36e-03 -1.23e-03 1\n",
"18 9.92e-04 7.36e-05 1.07e-03 -7.65e-04 -6.91e-04 1\n"
"0 9.51e-01 0.00e+00 9.51e-01 n/a n/a 2\n",
"1 9.24e-01 2.32e-03 9.27e-01 -2.70e-02 -2.47e-02 4\n",
"2 8.83e-01 3.53e-03 8.87e-01 -4.11e-02 -3.75e-02 4\n",
"3 8.23e-01 5.22e-03 8.28e-01 -6.06e-02 -5.54e-02 4\n",
"4 7.38e-01 7.39e-03 7.45e-01 -8.52e-02 -7.78e-02 5\n",
"5 6.26e-01 9.75e-03 6.36e-01 -1.11e-01 -1.01e-01 4\n",
"6 4.96e-01 1.16e-02 5.07e-01 -1.31e-01 -1.19e-01 4\n",
"7 3.62e-01 1.21e-02 3.74e-01 -1.34e-01 -1.22e-01 5\n",
"8 2.44e-01 1.09e-02 2.55e-01 -1.18e-01 -1.07e-01 4\n",
"9 1.53e-01 8.43e-03 1.62e-01 -9.03e-02 -8.19e-02 3\n",
"10 9.20e-02 5.80e-03 9.78e-02 -6.14e-02 -5.56e-02 4\n",
"11 5.35e-02 3.66e-03 5.72e-02 -3.85e-02 -3.48e-02 3\n",
"12 3.06e-02 2.19e-03 3.28e-02 -2.29e-02 -2.07e-02 3\n",
"13 1.73e-02 1.27e-03 1.86e-02 -1.33e-02 -1.20e-02 4\n",
"14 9.79e-03 7.24e-04 1.05e-02 -7.55e-03 -6.82e-03 3\n",
"15 5.52e-03 4.10e-04 5.93e-03 -4.27e-03 -3.86e-03 3\n",
"16 3.11e-03 2.31e-04 3.35e-03 -2.41e-03 -2.18e-03 3\n",
"17 1.76e-03 1.30e-04 1.89e-03 -1.36e-03 -1.23e-03 4\n",
"18 9.92e-04 7.36e-05 1.07e-03 -7.65e-04 -6.91e-04 4\n"
]
}
],
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"text/plain": [
"Krotov Optimization Result\n",
"--------------------------\n",
"- Started at 2020-03-22 16:55:24\n",
"- Started at 2020-03-24 14:43:50\n",
"- Number of objectives: 1\n",
"- Number of iterations: 18\n",
"- Reason for termination: Reached convergence: J_T < 1e-3\n",
"- Ended at 2020-03-22 16:55:53 (0:00:29)"
"- Ended at 2020-03-24 14:45:10 (0:01:20)"
]
},
"execution_count": 15,
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36 changes: 18 additions & 18 deletions docs/notebooks/02_example_lambda_system_rwa_complex_pulse.ipynb
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Expand Up @@ -16,12 +16,12 @@
"name": "stdout",
"output_type": "stream",
"text": [
"krotov 1.0.0+dev\n",
"scipy 1.3.1\n",
"matplotlib.pylab 1.17.2\n",
"qutip 4.4.1\n",
"krotov 1.1.0\n",
"matplotlib 3.2.1\n",
"qutip 4.5.0\n",
"numpy 1.17.2\n",
"scipy 1.3.1\n",
"CPython 3.7.6\n",
"IPython 7.13.0\n"
]
Expand Down Expand Up @@ -750,19 +750,19 @@
"output_type": "stream",
"text": [
"iter. J_T g_a_int_1 g_a_int_2 g_a_int_3 g_a_int_4 g_a_int J Delta J_T Delta J secs\n",
"0 1.01e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 1.01e+00 n/a n/a 1\n",
"1 6.72e-01 1.72e-01 5.72e-04 1.63e-01 7.44e-04 3.37e-01 1.01e+00 -3.37e-01 -2.83e-05 2\n",
"2 4.02e-01 1.44e-01 8.41e-04 1.24e-01 8.40e-04 2.70e-01 6.72e-01 -2.70e-01 -3.32e-05 2\n",
"3 2.22e-01 9.81e-02 9.26e-04 7.98e-02 7.75e-04 1.80e-01 4.02e-01 -1.80e-01 -3.55e-05 2\n",
"4 1.17e-01 5.78e-02 7.70e-04 4.58e-02 6.02e-04 1.05e-01 2.22e-01 -1.05e-01 -3.11e-05 2\n",
"5 6.00e-02 3.13e-02 5.35e-04 2.46e-02 4.20e-04 5.68e-02 1.17e-01 -5.69e-02 -2.30e-05 2\n",
"6 3.05e-02 1.62e-02 3.40e-04 1.27e-02 2.78e-04 2.95e-02 6.00e-02 -2.95e-02 -1.51e-05 2\n",
"7 1.54e-02 8.16e-03 2.11e-04 6.47e-03 1.82e-04 1.50e-02 3.05e-02 -1.50e-02 -9.25e-06 2\n",
"8 7.85e-03 4.08e-03 1.33e-04 3.25e-03 1.20e-04 7.59e-03 1.54e-02 -7.59e-03 -5.45e-06 2\n",
"9 4.03e-03 2.03e-03 8.59e-05 1.63e-03 8.01e-05 3.83e-03 7.85e-03 -3.83e-03 -3.15e-06 2\n",
"10 2.09e-03 1.01e-03 5.76e-05 8.13e-04 5.45e-05 1.94e-03 4.02e-03 -1.94e-03 -1.81e-06 2\n",
"11 1.10e-03 5.03e-04 3.97e-05 4.06e-04 3.76e-05 9.87e-04 2.09e-03 -9.88e-04 -1.04e-06 2\n",
"12 5.91e-04 2.51e-04 2.79e-05 2.03e-04 2.62e-05 5.09e-04 1.10e-03 -5.09e-04 -6.04e-07 2\n"
"0 1.01e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 0.00e+00 1.01e+00 n/a n/a 2\n",
"1 6.72e-01 1.72e-01 5.72e-04 1.63e-01 7.44e-04 3.37e-01 1.01e+00 -3.37e-01 -2.83e-05 5\n",
"2 4.02e-01 1.44e-01 8.41e-04 1.24e-01 8.40e-04 2.70e-01 6.72e-01 -2.70e-01 -3.32e-05 4\n",
"3 2.22e-01 9.81e-02 9.26e-04 7.98e-02 7.75e-04 1.80e-01 4.02e-01 -1.80e-01 -3.55e-05 5\n",
"4 1.17e-01 5.78e-02 7.70e-04 4.58e-02 6.02e-04 1.05e-01 2.22e-01 -1.05e-01 -3.11e-05 6\n",
"5 6.00e-02 3.13e-02 5.35e-04 2.46e-02 4.20e-04 5.68e-02 1.17e-01 -5.69e-02 -2.30e-05 6\n",
"6 3.05e-02 1.62e-02 3.40e-04 1.27e-02 2.78e-04 2.95e-02 6.00e-02 -2.95e-02 -1.51e-05 5\n",
"7 1.54e-02 8.16e-03 2.11e-04 6.47e-03 1.82e-04 1.50e-02 3.05e-02 -1.50e-02 -9.25e-06 6\n",
"8 7.85e-03 4.08e-03 1.33e-04 3.25e-03 1.20e-04 7.59e-03 1.54e-02 -7.59e-03 -5.45e-06 4\n",
"9 4.03e-03 2.03e-03 8.59e-05 1.63e-03 8.01e-05 3.83e-03 7.85e-03 -3.83e-03 -3.15e-06 5\n",
"10 2.09e-03 1.01e-03 5.76e-05 8.13e-04 5.45e-05 1.94e-03 4.02e-03 -1.94e-03 -1.81e-06 4\n",
"11 1.10e-03 5.03e-04 3.97e-05 4.06e-04 3.76e-05 9.87e-04 2.09e-03 -9.88e-04 -1.04e-06 5\n",
"12 5.91e-04 2.51e-04 2.79e-05 2.03e-04 2.62e-05 5.09e-04 1.10e-03 -5.09e-04 -6.04e-07 5\n"
]
}
],
Expand Down Expand Up @@ -803,11 +803,11 @@
"text/plain": [
"Krotov Optimization Result\n",
"--------------------------\n",
"- Started at 2020-03-22 16:56:05\n",
"- Started at 2020-03-24 14:45:22\n",
"- Number of objectives: 1\n",
"- Number of iterations: 12\n",
"- Reason for termination: Reached convergence: J_T < 0.001\n",
"- Ended at 2020-03-22 16:56:37 (0:00:32)"
"- Ended at 2020-03-24 14:46:29 (0:01:07)"
]
},
"execution_count": 20,
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Expand Up @@ -26,12 +26,12 @@
"name": "stdout",
"output_type": "stream",
"text": [
"numpy 1.17.2\n",
"matplotlib.pylab 1.17.2\n",
"scipy 1.3.1\n",
"krotov 1.1.0\n",
"matplotlib 3.2.1\n",
"qutip 4.4.1\n",
"krotov 1.0.0+dev\n",
"qutip 4.5.0\n",
"numpy 1.17.2\n",
"matplotlib.pylab 1.17.2\n",
"CPython 3.7.6\n",
"IPython 7.13.0\n"
]
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24 changes: 12 additions & 12 deletions docs/notebooks/04_example_dissipative_qubit_reset.ipynb
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Expand Up @@ -26,12 +26,12 @@
"name": "stdout",
"output_type": "stream",
"text": [
"matplotlib 3.2.1\n",
"numpy 1.17.2\n",
"scipy 1.3.1\n",
"qutip 4.4.1\n",
"krotov 1.0.0+dev\n",
"krotov 1.1.0\n",
"matplotlib.pylab 1.17.2\n",
"matplotlib 3.2.1\n",
"qutip 4.5.0\n",
"numpy 1.17.2\n",
"CPython 3.7.6\n",
"IPython 7.13.0\n"
]
Expand Down Expand Up @@ -805,7 +805,7 @@
" S(t) (ranges): [0.000000, 1.000000]\n",
" iter_start: 0\n",
" iter_stop: 5\n",
" duration: 0.6 secs (started at 2020-03-22 16:58:51)\n",
" duration: 0.9 secs (started at 2020-03-24 14:50:37)\n",
" optimized pulses (ranges): [0.00, 2.00]\n",
" ∫gₐ(t)dt: 0.00e+00\n",
" λₐ: 1.00e-02\n",
Expand All @@ -814,7 +814,7 @@
" τ: (7.97e-01:0.00π)\n",
" qubit error: 1.1e-01\n",
"Iteration 1\n",
" duration: 2.8 secs (started at 2020-03-22 16:58:51)\n",
" duration: 2.8 secs (started at 2020-03-24 14:50:38)\n",
" optimized pulses (ranges): [0.00, 2.06]\n",
" ∫gₐ(t)dt: 7.72e-02\n",
" λₐ: 1.00e-02\n",
Expand All @@ -823,7 +823,7 @@
" τ: (7.98e-01:0.00π)\n",
" qubit error: 1.1e-01\n",
"Iteration 2\n",
" duration: 3.3 secs (started at 2020-03-22 16:58:54)\n",
" duration: 2.9 secs (started at 2020-03-24 14:50:41)\n",
" optimized pulses (ranges): [0.00, 2.23]\n",
" ∫gₐ(t)dt: 5.72e-01\n",
" λₐ: 1.00e-02\n",
Expand All @@ -832,7 +832,7 @@
" τ: (8.01e-01:0.00π)\n",
" qubit error: 6.7e-02\n",
"Iteration 3\n",
" duration: 3.1 secs (started at 2020-03-22 16:58:57)\n",
" duration: 3.2 secs (started at 2020-03-24 14:50:44)\n",
" optimized pulses (ranges): [0.00, 2.33]\n",
" ∫gₐ(t)dt: 8.11e-02\n",
" λₐ: 1.00e-02\n",
Expand All @@ -841,7 +841,7 @@
" τ: (7.99e-01:0.00π)\n",
" qubit error: 5.0e-02\n",
"Iteration 4\n",
" duration: 3.1 secs (started at 2020-03-22 16:59:00)\n",
" duration: 2.7 secs (started at 2020-03-24 14:50:47)\n",
" optimized pulses (ranges): [0.00, 2.19]\n",
" ∫gₐ(t)dt: 2.16e-01\n",
" λₐ: 1.00e-02\n",
Expand All @@ -850,7 +850,7 @@
" τ: (8.02e-01:0.00π)\n",
" qubit error: 4.9e-02\n",
"Iteration 5\n",
" duration: 3.2 secs (started at 2020-03-22 16:59:03)\n",
" duration: 3.4 secs (started at 2020-03-24 14:50:50)\n",
" optimized pulses (ranges): [0.00, 2.15]\n",
" ∫gₐ(t)dt: 6.38e-02\n",
" λₐ: 1.00e-02\n",
Expand Down Expand Up @@ -898,11 +898,11 @@
"text/plain": [
"Krotov Optimization Result\n",
"--------------------------\n",
"- Started at 2020-03-22 16:58:51\n",
"- Started at 2020-03-24 14:50:37\n",
"- Number of objectives: 1\n",
"- Number of iterations: 5\n",
"- Reason for termination: Reached 5 iterations\n",
"- Ended at 2020-03-22 16:59:07 (0:00:16)"
"- Ended at 2020-03-24 14:50:53 (0:00:16)"
]
},
"execution_count": 20,
Expand Down
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