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Rapid development of novel quantum algorithms

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Tequila is an Extensible Quantum Information and Learning Architecture where the main goal is to simplify and accelerate implementation of new ideas for quantum algorithms. It operates on abstract data structures allowing the formulation, combination, automatic differentiation and optimization of generalized objectives. Tequila can execute the underlying quantum expectation values on state of the art simulators as well as on real quantum devices.

You can get an overview from this presentation or from it's video recording

Get started with our Tutorials

or checkout our overview article

Quantum Backends

Currently supported - Qulacs - Qibo - Qiskit - Cirq - PyQuil

Tequila detects backends automatically if they are installed on your systems.
All of them are available over standard pip installation like for example

pip install qulacs
For best performance it is recommended to have


Currently supported - Psi4.
In a conda environment this can be installed with

conda install psi4 -c psi4
Here is a small tutorial that illustrates the usage.
  • Madness
    Currently you need to compile from a separate fork.
    See the github page of this fork for installation instruction.
    Note that the madness interface is currently only available on the
    branch of tequila (coming to master soon).
    Here is a small tutorial that illustrates the usage.


We recommend installing in editable mode with

git clone
cd tequila
pip install -e . 

Do not install over PyPi (Minecraft lovers excluded)

pip install tequila

You can install

directly with pip over:
pip install git+

Recommended Python version is 3.7 or 3.6.
Python 3.8 works, but not all (optional) dependencies support it yet.

Getting Started

Check out the tutorial notebooks provided in tutorials.

Tequila Hello World

# optimize a one qubit example

define a variable

a = tq.Variable("a")

define a simple circuit

U = tq.gates.Ry(angle=a*pi, target=0)

define an Hamiltonian

H = tq.paulis.X(0)

define an expectation value

E = tq.ExpectationValue(H=H, U=U)

optimize the expectation value

result = tq.minimize(method="bfgs", objective=E**2)

check out the optimized wavefunction

wfn = tq.simulate(U, variables=result.angles) print("optimized wavefunction = ", wfn)

plot information about the optimization

result.history.plot("energies") result.history.plot("angles") result.history.plot("gradients")

Chemistry Hello World

# define a molecule within an active space
active = {"a1": [1], "b1":[0]}
molecule = tq.quantumchemistry.Molecule(geometry="", basis_set='6-31g', active_orbitals=active, transformation="bravyi-kitaev")

get the qubit hamiltonian

H = molecule.make_hamiltonian()

create an k-UpCCGSD circuit of order k

U = molecule.make_upccgsd_ansatz(order=1, include_singles=True)

define the expectationvalue

E = tq.ExpectationValue(H=H, U=U)

compute reference energies

fci = molecule.compute_energy("fci") cisd = molecule.compute_energy("detci", options={"detci__ex_level": 2})


result = tq.minimize(objective=E, method="BFGS", initial_values=0.0)

print("VQE : {:+2.8}f".format( print("CISD: {:+2.8}f".format(cisd)) print("FCI : {:+2.8}f".format(fci))

Do you want to create your own methods? Check out the tutorials!

Research projects using Tequila

J.S. Kottmann, A. Anand, A. Aspuru-Guzik.
A Feasible Approach for Automatically Differentiable Unitary Coupled-Cluster on Quantum Computers.
Chemical Science, 2021,
General techniques are implemented in the chemistry modules of tequila.
See the tutorials for examples.

J.S. Kottmann, P. Schleich, T. Tamayo-Mendoza, A. Aspuru-Guzik.
Reducing Qubit Requirements while Maintaining Numerical Precision for the Variational Quantum Eigensolver: A Basis-Set-Free Approach.
J.Phys.Chem.Lett., 2021, example code tutorial on the madness interface

A. Cervera-Lierta, J.S. Kottmann, A. Aspuru-Guzik.
The Meta-Variational Quantum Eigensolver. example code

J.S. Kottmann, M. Krenn, T.H. Kyaw, S. Alperin-Lea, A. Aspuru-Guzik.
Quantum Computer-Aided design of Quantum Optics Hardware. example code

A. Anand, M. Degroote, A. Aspuru-Guzik.
Natural Evolutionary Strategies for Variational Quantum Computation.

Let us know, if you want your research project to be included in this list!


Support for additional optimizers can be activated by intalling them in your environment.
Tequila will then detect them automatically.
Currently those are: Phoenics and GPyOpt.


You can build the documentation by navigating to

and entering
make html
Open the documentation with a browser over like
firefox docs/build/html/index.html

Note that you will need some additional python packages like
that are not explicitly listed in the requirements.txt

You can also visit our prebuild online documentation
that will correspond to the github master branch

How to contribute

If you find any bugs or inconveniences in

please don't be shy and let us know.
You can do so either by raising an issue here on github or contact us directly.

If you already found a solution you can contribute to

over a pull-request.
Here is how that works:
  1. Make a fork of
    to your own github account.
  2. Checkout the
    branch and make sure it is up to date with the main github repository.
  3. Create and checkout a new branch from
    git branch pr-my-branch-name
    followed by
    git checkout pr-my-branch-name
    . By typing
    git branch
    afterwards you can check which branch is currently checked out on your computer.
  4. Introduce changes to the code and commit them with git.
  5. Push the changes to your github account
  6. Log into github and create a pull request to the main github repository. The pull-request should be directed to the
    branch (but we can also change that afterwards).

If you plan to introduce major changes to the base library it can be beneficial to contact us first.
This way we might be able to avoid conflicts before they arise.

If you used

for your research, feel free to include your algoritms here, either by integrating it into the core libraries or by demonstrating it with a notebook in the tutorials section. If you let us know about it, we will also add your research article in the list of research projects that use tequila (see above).


If you experience trouble of any kind or if you either want to implement a new feature or want us to implement a new feature that you need:
don't hesitate to contact us directly or raise an issue here on github

Qulacs simulator

You will need cmake to install the qulacs simulator

pip install cmake

You don't need

for tequila to run (although is is recommended)
To install without
just remove the
line from

It can be replaced by one (or many) of the other supported simulators.
Note that simulators can also be installed on a later point, they don't need to be installed with
As long as they are installed within the same python environment
can detect them.


You can in principle use tequila with windows as OS and have almost full functionality.
You will need to replace

for it to work.
In order to do so: Remove
and add

In order to install qulacs you will need latest GNU compilers (at least gcc-7).
They can be installed for example over visual studio.

Mac OS

Tequila runs on Macs OSX.
You might get in trouble with installing qulacs since it currently does not work with Apple's clang compiler.
You need to install latest GNU compile (at least gcc-7 and g++7) and set them as default before installing qulacs over pip.

Qibo and GPyOpt

Currently you can't use Qibo and GPyOpt within the same environment

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