Contributions are welcome, and they are greatly appreciated! Every little bit helps, and credit will always be given.

Code of Conduct

Everyone interacting in the krotov project’s code base, issue tracker, and any communication channels is expected to follow the PyPA Code of Conduct.

Report Bugs

Report bugs at

If you are reporting a bug, please include:

  • Your operating system name and version.

  • Any details about your local setup that might be helpful in troubleshooting.

  • Detailed steps to reproduce the bug.

Submit Feedback

The best way to send feedback is to file an issue at

If you are proposing a feature:

  • Explain in detail how it would work.

  • Keep the scope as narrow as possible, to make it easier to implement.

  • Remember that this is a volunteer-driven project, and that contributions are welcome :)

Pull Request Guidelines

Before you submit a pull request, check that it meets these guidelines:

  1. The pull request should include tests.

  2. If the pull request adds functionality, the docs should be updated. Put your new functionality into a function with a docstring, and add the feature to the list in docs/04_features.rst and/or HISTORY.rst.

  3. Check and make sure that the tests pass for all supported Python versions.

Get Started!

Ready to contribute? Follow Aaron Meurer’s Git Workflow Notes (with qucontrol/krotov instead of sympy/sympy)

In short, if you are not a member of the qucontrol organization,

  1. Clone the repository from

  2. Fork the repo on GitHub to your personal account.

  3. Add your fork as a remote.

  4. Pull in the latest changes from the master branch.

  5. Create a topic branch.

  6. Make your changes and commit them (testing locally).

  7. Push changes to the topic branch on your remote.

  8. Make a pull request against the base master branch through the Github website of your fork.

The project uses tox for automated testing accross multiple versions of Python and for various development tasks such as linting and generating the documentation. See Development Prerequisites for details.

There is also a Makefile that wraps around tox, for convenience on Unix-based systems. In your checked-out clone, run

$ make help

to see the available make targets. If you cannot use make, but want to use tox directly (e.g., on Windows), run

$ tox -av

to see a list of tox environments and a description. For the initial configuration of tox environments, you may have to run

$ tox -e bootstrap

in order to set up the tox.ini configuration file.

If you are a member of the qucontrol organization, there is no need to fork krotov - you can directly pull and push to

Development Prerequisites

Contributing to the package’s developments requires that you have Python 3.7 and tox installed. It is strongly recommended that you also have installations of all other supported Python versions. The recommended way to install multiple versions of Python at the same time is through pyenv (or pyenv-win on Windows).

Alternatively, you may install conda (via the Anaconda or Miniconda distributions, or also through pyenv). As conda can create environments with any version of Python (independent of which Python version conda was originally installed with), this alleviates the need for managing multiple versions. The advantage of using conda is that you may be able to avoid installing the compilers necessary for Python extension packages. The disadvantage is that environment creation is slower and the resulting environments are bigger, and that you may run into occasional binary incompatibilities between conda packages.


If you want to use conda, you must use the tox-conda.ini configuration file. That is, run all make comands as e.g. make TOXINI=tox-conda.ini test and tox commands as e.g. tox -c tox-conda.ini -e py35-test,py36-test,py37-test. Alternatively, make tox-conda.ini the default by copying it to tox.ini.

Branching Model

For developers with direct access to the repository, krotov uses a simple branching model where all developments happens directly on the master branch. Releases are tags on master. All commits on master should pass all tests and be well-documented. This is so that git bisect can be effective. For any non-trivial issue, it is recommended to create a topic branch, instead of working on master. There are no restrictions on commits on topic branches, they do not need to contain complete documentation, pass any tests, or even be able to run.

To create a topic-branch named issue1:

$ git branch issue1
$ git checkout issue1

You can then make commits, and push them to Github to trigger Continuous Integration testing:

$ git push -u origin issue1

Commit early and often! At the same time, try to keep your topic branch as clean and organized as possible. If you have not yet pushed your topic branch to the “origin” remote:

  • Avoid having a series of meaningless granular commits like “start bugfix”, “continue development”, “add more work on bugfix”, “fix typos”, and so forth. Instead, use git commit --amend to add to your previous commit. This is the ideal way to “commit early and often”. You do not have to wait until a commit is “perfect”; it is a good idea to make hourly/daily “snapshots” of work in progress. Amending a commit also allows you to change the commit message of your last commit.

  • You can combine multiple existing commits by “squashing” them. For example, use git rebase -i HEAD~4 to combined the previous four commits into one. See the “Rewriting History” section of Pro Git book for details (if you feel this is too far outside of your git comfort zone, just skip it).

  • If you work on a topic branch for a long time, and there is significant work on master in the meantime, periodically rebase your topic branch on the current master (git rebase master). Avoid merging master into your topic branch. See Merging vs. Rebasing.

If you have already pushed your topic branch to the remote origin, you have to be a bit more careful. If you are sure that you are the only one working on that topic branch, you can still follow the above guidelines, and force-push the issue branch (git push --force). This also applies if you are an external contributor preparing a pull request in your own clone of the project. If you are collaborating with others on the topic branch, coordinate with them whether they are OK with rewriting the history. If not, merge instead of rebasing. You must never rewrite history on the master branch (nor will you be able to, as the master branch is “protected” and can only be force-pushed to in coordination with the project maintainer). If something goes wrong with any advanced “history rewriting”, there is always “git reflog” as a safety net – you will never lose work that was committed before.

When you are done with a topic branch (the issue has been fixed), finish up by merging the topic branch back into master:

$ git checkout master
$ git merge --no-ff issue1

The --no-ff option is critical, so that an explicit merge commit is created (especially if you rebased). Summarize the changes of the branch relative to master in the commit message.

Then, you can push master and delete the topic branch both locally and on Github:

$ git push origin master
$ git push --delete origin issue1
$ git branch -D issue1

Commit Message Guidelines

Write commit messages according to this template:

Short (50 chars or less) summary ("subject line")

More detailed explanatory text. Wrap it to 72 characters. The blank
line separating the summary from the body is critical (unless you omit
the body entirely).

Write your subject line in the imperative: "Fix bug" and not "Fixed
bug" or "Fixes bug." This convention matches up with commit messages
generated by commands like git merge and git revert. A properly formed
git commit subject line should always be able to complete the sentence
"If applied, this commit will <your subject line here>".

Further paragraphs come after blank lines.

- Bullet points are okay, too.
- Typically a hyphen or asterisk is used for the bullet, followed by a
  single space. Use a hanging indent.

You should reference any issue that is being addressed in the commit, as
e.g. "#1" for issue #1. If the commit closes an issue, state this on the
last line of the message (see below). This will automatically close the
issue on Github as soon as the commit is pushed there.

Closes #1

See Closing issues using keywords for details on references to issues that Github will understand.


The Krotov package includes a full test-suite using pytest. We strive for a test coverage above 90%.

From a checkout of the krotov repository, you can use

$ make test

to run the entire test suite, or

$ tox -e py35-test,py36-test,py37-test

if make is not available.

The tests are organized in the tests subfolder. It includes python scripts whose name start with test_, which contain functions whose names also start with test_. Any such functions in any such files are picked up by pytest for testing. In addition, doctests from any docstring or any documentation file (*.rst) are picked up (by the pytest doctest plugin). Lastly, all example notebooks are validated as a test, through the nbval plugin.

Code Style

All code must be compatible with PEP 8. The line length limit is 79 characters, although exceptions are permissible if this improves readability significantly.

Beyond PEP 8, this project adopts the Black code style, with --skip-string-normalization --line-length 79. You can run make black-check or tox -e run-blackcheck to check adherence to the code style, and make black or tox -e run-black to apply it.

Imports within python modules must be sorted according to the isort configuration in setup.cfg. The command make isort-check or tox -e run-isortcheck checks whether all imports are sorted correctly, and make isort or tox -e run-isort modifies all Python modules in-place with the proper sorting.

The code style is enforced as part of the test suite, as well as through git pre-commit hooks that prevent committing code not does not meet the requirements. These hooks are managed through the pre-commit framework.


After cloning the krotov repository, you should run make bootstrap, tox -e bootstrap, or python scripts/ from within the project root folder. These set up tox, and the pre-commit hooks

You may use make flake8-check or tox -e run-flake8 and make pylint-check or tox -e run-pylint for additional checks on the code with flake8 and pylint, but there is no strict requirement for a perfect score with either one of these linters. They only serve as a guideline for code that might be improved.

Write Documentation

The krotov package could always use more documentation, whether as part of the official docs, in docstrings, or even on the web in blog posts, articles, and such.

The package documentation is generated with Sphinx, the documentation (and docstrings) are formatted using the Restructured Text markup language (file extension rst). See also the Matplotlib Sphinx cheat sheet for some helpful tips.

Each function or class must have a docstring; this docstring must be written in the “Google Style” format (as implemented by Sphinx’ napoleon extension). Docstrings and any other part of the documentation can include mathematical formulas in LaTeX syntax (using mathjax). In addition to Sphinx’ normal syntax for inline math (:math:`x`), you may also use easier-to-read dollar signs ($x$). The Krotov package defines some custom tex macros for quantum mechanics, which you are strongly encouraged to use. These include:

  • \bra, e.g. $\bra{\Psi}$ for \(\bra{\Psi}\) (or \\Bra{} for auto-resizing). Do not use \langle/\rangle/\vert manually!

  • \ket, e.g. $\ket{\Psi}$ for \(\ket{\Psi}\) (or \Ket{} for auto-resizing).

  • \Braket, e.g. $\Braket{\Phi}{\Psi}$ for \(\Braket{\Phi}{\Psi}\).

  • \Op for quantum operators, e.g. $\Op{H}$ for \(\Op{H}\).

  • \Abs for absolute values, e.g. $\Abs{x}$ for \(\Abs{x}\).

  • \AbsSq for the absolute-square, e.g. $\AbsSq{\Braket{\Phi}{\Psi}}$ for \(\AbsSq{\Braket{\Phi}{\Psi}}\).

  • \avg for the expectation values, e.g. $\avg{\Op{H}}$ for \(\avg{\Op{H}}\) (or \Avg{} for auto-resizing).

  • \Norm for the norm, e.g. $\Norm{\ket{\Psi}}$ for \(\Norm{\ket{\Psi}}\).

  • \identity for the identity operator, \(\identity\).

  • \Liouville for the Liouvillian symbol, \(\Liouville\).

  • \DynMap for the symbolic dynamical map, \(\DynMap\).

  • \dd for the differential, e.g. $\int f(x) \dd x$ for \(\int f(x) \dd x\).

  • Function names / mathematical operators \tr, \diag, \abs, \pop.

  • Text labels \aux, \opt, \tgt, \init, \lab, \rwa.

Also see Math in Example Notebooks.

You may use the BibTeX plugin for citations.

At any point, from a checkout of the krotov repository, you may run

$ make docs


$ tox -e docs

to generate the documentation locally.

Deploy the documentation

The documentation is automatically deployed to (the gh-pages associated with the krotov package’s Github repository) every time commits are pushed to Github. This is done via the Travis Continuous Integration service and Doctr. The documentation for all versions of krotov is visible on the gh-pages git branch. Any changes that are committed and pushed from this branch will be deployed to the online documentation. Do not routinely perform manual edits on the gh-pages branch! Let Doctr do its job of automatically deploying documentation instead.

The deployment of the documentation is set up roughly as follows:

  • In .travis.yml, there is “Docs” job set up that executes the .travis/ script.

  • The .travis/ script builds the HTML documentation, as well as downloadable versions of the documentation (tagged released only!). It then calls doctr deploy to deploy to gh-pages.

  • doctr deploy copies the built documentation to the appropriate subfolder on gh-pages. It then gets the script .travis/ script from the release branch and executes it.

  • The .travis/ script (using the .travis/ module) analyzes all folders on gh-pages and generates a versions.json file on gh-pages. This file contains all the information required to render the navigation menu in the bottom left corner of the online documentation. That menu is rendered by the javascript in ./docs/_static/version-menu.js (cf. html_js_files = ["version-menu.js"] in docs/ The .travis/ script also generates an index.html pointing to the most recent stable release.

  • doctr deploy commits the rendered documentation as well as the versions.json and index.html files and pushes the gh-pages branch. It does this using the deploy key in ./docs/doctr_deploy_key.enc. That file contains the private key matching the public doctr key in The private key itself is encrypted with Travis’ public key, so that only Travis can decrypt it with their private key, and use it to authenticate while pushing to gh-pages.

Contribute Examples

Examples should be contributed in the form of Jupyter notebooks.

Example notebooks are automatically rendered as part of the documentation (Examples), and they are also verified by the automated tests. For this to work properly, the following steps must be taken:

  • Put all imports near the top of the notebook, with # NBVAL_IGNORE_OUTPUT as the first line. Use the watermark package to print out the versions of imported packages. For example:

    %load_ext watermark
    import qutip
    import numpy as np
    import scipy
    import matplotlib
    import matplotlib.pylab as plt
    %watermark -v --iversions
  • Put the notebook in the folder docs/notebooks/.

  • Before committing, re-evaluate all example notebooks in a well-defined virtual environment by running

    $ make notebooks
  • Check that the examples can be verified across different Python version by running

    $ make test
  • You may also verify that the example is properly integrated in the documentation by running

    $ make docs

Math in Example Notebooks

You may use the same tex macros described in the Write Documentation section. However, for the macros to work when viewing the notebook by itself, they must be redefined locally. To this end, add a markdown cell underneath the top cell that contains the imported packages (see above). The cell must contain the following:

\newcommand{Braket}[2]{\left\langle #1\vphantom{#2} \mid #2\vphantom{#1}\right\rangle}

Upon executing the cell the definitions will be hidden, but the defined macros will be available in any cell in the rest of the notebook.


Releases should follow Semantic Versioning, and version numbers published to PyPI must be compatible with PEP 440.

In short, versions number follow the pattern major.minor.patch, e.g. 0.1.0 for the first release, and 1.0.0 for the first stable release. If necessary, pre-release versions might be published as e.g:

1.0.0-dev1  # developer's preview 1 for release 1.0.0
1.0.0-rc1   # release candidate 1 for 1.0.0

Errors in the release metadata or documentation only may be fixed in a post-release, e.g.:

1.0.0.post1  # first post-release after 1.0.0

Post-releases should be used sparingly, but they are acceptable even though they are not supported by the Semantic Versioning specification.

The current version is available through the __version__ attribute of the krotov package:

>>> import krotov
>>> krotov.__version__   

Between releases, __version__ on the master branch should either be the version number of the last release, with “+dev” appended (as a “local version identifier”), or the version number of the next planned release, with “-dev” appended (“pre-release identifier” with extra dash). The version string “1.0.0-dev1+dev” is a valid value after the “1.0.0-dev1” pre-release. The “+dev” suffix must never be included in a release to PyPI.

Note that twine applies normalization to the above recommended forms to make them strictly compatible with PEP 440, before uploading to PyPI. Users installing the package through pip may use the original version specification as well as the normalized one (or any other variation that normalizes to the same result).

When making a release via

$ make release

the above versioning conventions will be taken into account automatically.

Releases must be tagged in git, using the version string prefixed by “v”, e.g. v1.0.0-dev1 and v1.0.0. This makes them available at

Developers’ How-Tos

The following assumes your current working directory is a checkout of krotov, and that you have successfully run make test (which creates the tox environments that development relies on).

How to run a jupyter notebook server for working on the example notebooks

A notebook server that is isolated to the proper testing environment can be started via the Makefile:

$ make jupyter-notebook

This is equivalent to:

$ tox -e run-cmd -- jupyter notebook --config=/dev/null

You may run this with your own options, if you prefer. The --config=/dev/null guarantees that the notebook server is completely isolated. Otherwise, configuration files from your home directly (see Jupyter’s Common Configuration system) may influence the server. Of course, if you know what you’re doing, you may want this.

If you prefer, you may also use the newer jupyterlab:

$ make jupyter-lab

How to convert an example notebook to a script for easier debugging

Interactive debugging in notebooks is difficult. It becomes much easier if you convert the notebook to a script first. To convert a notebook to an (I)Python script and run it with automatic debugging, execute e.g.:

$ tox -e run-cmd -- jupyter nbconvert --to=python --stdout docs/notebooks/01_example_transmon_xgate.ipynb >
$ tox -e run-cmd -- ipython --pdb

You can then also set a manual breakpoint by inserting the following line anywhere in the code:

from IPython.terminal.debugger import set_trace; set_trace() # DEBUG

How to make git diff work for notebooks

Install nbdime and run nbdime config-git --enable --global to enable the git integration.

How to commit failing tests or example notebooks

The test-suite on the master branch should always pass without error. If you would like to commit any example notebooks or tests that currently fail, as a form of test-driven development, you have two options:

  • Push onto a topic branch (which are allowed to have failing tests), see the Branching Model. The failing tests can then be fixed by adding commits to the same branch.

  • Mark the test as failing. For normal tests, add a decorator:


    See the pytest documentation on skip and xfail for details.

    For notebooks, the equivalent to the decorator is to add a comment to the first line of the failing cell, either:


    (preferably), or:


    (this may affect subsequent cells, as the marked cell is not executed at all). See the documentation of the nbval pluging on skipping and exceptions for details.

How to run a subset of tests

To run e.g. only the tests defined in tests/, use any of the following:

$ make test TESTS=tests/

$ tox -e py37-test -- tests/

$ tox -e run-cmd -- pytest tests/

$ .tox/py37/bin/pytest tests/

See the pytest test selection docs for details.

How to run only as single test

Decorate the test with e.g., and then run, e.g:

$ tox -e run-cmd -- pytest -m xxx tests/

See the pytest documentation on markers for details.

How to run only the doctests

Run the following:

$ tox -e run-cmd -- pytest --doctest-modules src

How to go into an interactive debugger

Optionally, install the pdbpp package into the testing environment, for a better experience:

$ tox -e run-cmd -- pip install pdbpp


  • before the line where you went to enter the debugger, insert a line:

    from IPython.terminal.debugger import set_trace; set_trace() # DEBUG
  • Run pytest with the option -s, e.g.:

    $ tox -e run-cmd -- pytest -m xxx -s tests/

You may also see the pytest documentation on automatic debugging.

How to see the debug logger output in the example notebooks

The optimize_pulses() routine generates some logger messages for debugging purposes. To see these messages, set the level of “krotov” logger to INFO or DEBUG:

import logging
logger = logging.getLogger('krotov')

You can also configure the logger with custom formatters, e.g. to show the messages with time stamps:

ch = logging.StreamHandler()
formatter = logging.Formatter("%(asctime)s:%(message)s")
logging.getLogger().handlers = [] # disable root handlers

See the Configure Logging section of the Python documentation for more details.

How to use quantum mechanical tex macros

For docstrings or *.rst files, see Write Documentation. For notebooks, see Math in Example Notebooks.