Contextuality degree of quadrics in multi-qubit symplectic polar spaces
and
Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank
and
Three-Qubit-Embedded Split Cayley Hexagon is Contextuality Sensitive
Copyright (C) 2021-2022 Henri de Boutray
Contact: henrideboutray[at]hotmail.fr
About
The code has been developed to study quantum geometries generated with symplectic polar spaces in correspondence with the Pauli group. In particular, contextuality for the article [dHG+22] presented as a poster [dHG+21] for QPL’21, subspaces structures for the article [SdHG21] and the Cayley hexagon for the article [HdS22]. The language chosen was Magma since it is a well-established language for mathematics.
These articles are closely related to the content of the program files.
Installation
We give a heads up to the user: due to the way Magma is achitectured, installation is not trivial so some manual work is needed in order to run our code.
Two types of files are used in this project:
- files containing intrinsics, called packages
- and files containing “normal” function, called scripts
The intrinsics are typed and compiled function, their use allow us a greater
flexibility (as overloading), as well as the usual benefits of typing (earlier
error detection, safer usage, …). But since packages are compiled, they must
be treated differently to scripts. In order to deal with this, the simplest
solution is to put these files in a Magma source code folder. These folders are
listed in the system environment variable MAGMA_SYSTEM_SPEC accessible through
the Magma prompt with the command GetEnv("MAGMA_SYSTEM_SPEC");. But this may
be impossible for many reasons, in this case please refer to
this documentation
page to understand how to attach a package in Magma. You can obviously contact
me directly in case you cannot find out
how to attach the packages on your system. All packages are in the
src/intrinsics
folder.
Once the intrinsics attached, you can call them in scripts or in the Magma
shell. The Main_***.m files are such examples of scripts. All scripts are in the
src/mains
folder.
Assuming Magma is installed on your computer, here is a list of commands you may use to run our programs. Please keep in mind that they are not the only ones that will work and they are only meant to work on Unix-like systems. (You should understand commands copied from the web before running them!)
git clone https://github.com/quantcert/quantcert.github.io.git
cd quantcert.github.io/Magma-contextuality/src
touch ~/.bashrc
echo "export \"MAGMA_USER_SPEC=$(pwd)/intrinsics.spec\"" >> ~/.bashrc
source ~/.bashrc
cd mains
magma Main_AllContextualityChecks.m
Scripts to articles matching
As stated previously, the code follows closely the content of the corresponding papers.
The results described in Table 2 of [dHG+22] are given by the script Main_AllContextualityChecks.m.
[SdHG21] presenting a variety of results, several scripts were written to generate them. In particular:
- Sec. 4 is covered by the script Main_GeometryIntersections_3qubits.m;
- Sec. 5 is covered by the script Main_Heptads.m;
- Sec. 6 is covered by the script Main_GeometryIntersections_4qubits.m.
[HdS22]’s results (number of embeddings and contextuality of their complement) are obtainable by running the script Main_Skewed-Cayley-hexagon.m.
Copyright
This program is distributed under the GNU GPL 3. See the enclosed file LICENSE.
References
| [dHG+22] | Henri de Boutray, Frédéric Holweck, Alain Giorgetti, Pierre-Alain Masson and Metod Saniga. Contextuality degree of quadrics in multi-qubit symplectic polar spaces. https://doi.org/10.1088/1751-8121/aca36f, arXiv:2105.13798 |
| [dHG+21] | Henri de Boutray, Frédéric Holweck, Alain Giorgetti and Pierre-Alain Masson. Automated detection of contextuality proofs with intermediate numbers of observables. QPL’21, Poster |
| [SdHG21] | Metod Saniga, Henri de Boutray, Frédéric Holweck and Alain Giorgetti. Taxonomy of Polar Subspaces of Multi-Qubit Symplectic Polar Spaces of Small Rank. doi:10.3390/math9182272 |
| [HdS22] | Frédéric Holweck, Henri de Boutray and Metod Saniga. Three-Qubit-Embedded Split Cayley Hexagon is Contextuality Sensitive. doi:10.1038/s41598-022-13079-3 |