Mermin on Qiskit

With participation of Henri de Boutray

This project aims to use the Qiskit library to study entanglement in various cases. It contains files to easily run quantum algorithms (a light overhead has been added to the default Qiskit method used to submit jobs, in order to simplify this process), and evaluate states resulting of these algorithms using optimized Mermin operators.

Content of this project

The pipeline of the evaluation process is as follows:

1. Compute the optimized Mermin operator. The result will be stored as a list of parameters defining the monomials of the Mermin polynomial: ((a_1,a_2,...,a_n),(a'_1,a'_2,...,a'_n)) where each a_i or a'_i is a triplet of reals (see the article for more details).
2. Run the algorithm (either using the default Qiskit method, or better, by feeding the algorithm to the function that will also perform the evaluation and that wrap the Qiskit methods)
3. Evaluate the output state.

Two examples are given here on how to use this module:

1. In the QFT, each state of the execution is studied, but since we are in a quantum context, one cannot directly study the states from a single run, so the algorithm is split in a series of runs, for which each one contains only the first k gates, for k between 0 and the number of gates. In this process, the optimization was performed externally, by the mermin_eval module previously developed for sage. This module is not included in this project, but one can fetch it and use it externally, or ask the authors for more information.
2. For the graphstates, only the entanglement value of a graphstate was studied, so only one evaluation was needed. The optimization process is included in the module, in the submodule graphstates_opti.

Documentation

The code documentation can be found in pdf format or as a website. It is generated from the code using Sphinx.

Requirements

This module requires:

• Python 3.7+
• Qiskit 0.20.0

In order to build the documentation, the software Sphinx (version 1.8.5) has been used.

Run it

Docker

A Dockerfile has been produced in order to easily reproduce the results associated with this project. In order to use it, one must have Docker installed, and run the command docker build --tag sagemath:qiskit . from the folder containing the Dockerfile.

Once the image built, one can run it using the command:

docker run -it --mount type=bind,source=$(pwd)/app,target=/home/sage/app \
    sagemath:qiskit "sh -c 'cd /home/sage/app; bash'"

(Change the $(pwd)/app with a path compatible with you OS, for example on Windows it would be %cd%/app)

with this command, your environment is all set to run everything you want to, and the files are dynamically mounted so you can edit them on your favorite editor, and run them from the container.

Since the process of running the various files is made transparent, the rest of the description on how to run the project will be provided in the following section.

On your machine directly

If you installed the requirements, you can also skip Docker and run the various files directly on your computer.

We encourage you to explore the various files provided. And for an example on how to use them, you can go to the folder examples and run

python QFT-4-1-1.py

or

python graphstates.py

To rebuild the documentation, just type make doc-html or make doc-latexpdf in the app folder, the result will be in doc/build.