Qontextium

Qontextium is a program which estimates the contextuality degree of quantum configurations. It is developed in the C language and is using the OpenMP parallelization library.

Copyright (C) 2024 Axel Muller and Alain Giorgetti.

Université de Franche-Comté, CNRS, institut FEMTO-ST, F-25000 Besançon, France

Contact: axel.muller AT femto-st.fr

Copyright

This program is distributed under the GNU GPL 2. See the enclosed file LICENSE.

Installation

Linux is required to run this program. The program is located in this folder. flex and bison need to be installed in your machine for the program to run. These tools are commonly available and easy to install on most Linux distributions. If you don’t have them already, you can typically install them using your distribution’s package manager. For example, on Debian-based systems:

sudo apt-get install flex bison

The compilation is automatic when running Qontextium for the first time.

Execution

Here are the possible options to execute the program:

./qontextium CONFIGURATION [OPTIONS] [--solver SOLVER] [--export VAL] [--no-interaction]

QUBITS_NUMBER is the number of qubits in the configuration.

--export [all|valid|invalid]:      exports the requested contexts to the standard output in the CSV format

–no-interaction: disables the interactions with the user after the computations (useful for scripts)

CONFIGURATION [OPTIONS] is the configuration to be generated. It can be one of the following:

–import assignment [FILE]: imports a configuration from a file (see ./misc/qa_grid.txt for an example) and estimates its contextuality degree

–import hypergram [FILE1] [FILE2]: imports a hypergram from two files, checks assignability. When assignable, estimates the contextuality degree. The first file describes the hypergraph. The second file describes a Gram matrix on the same vertices (see ./misc/grid.hypergraph.txt and ./misc/grid.gram.txt for an example)

–elliptic n [–complement]: generates n qubit elliptic configurations (or their complement or all of them)

–hyperbolic n [–complement]: generates n qubit hyperbolic configurations (or their complement or all of them)

–perpset n [–complement]: generates n qubit perpsets configurations (or their complement or all of them)

–subspaces k n: generates a n qubit configuration with all subspaces of dimension k as contexts

–affine n: generates n qubit affine configurations

–hexagon [skew] [–complement

–all]: generates classical or skew embeddings of split cayley hexagons

SOLVER

–solver sat: uses a SAT solver to estimate the contextuality degree (eventually gives the optimum)

–solver heuristic: uses the heuristic method presented in MSGHK24 to estimate the contextuality degree (faster, but no guarantee of finding the optimum)

–solver retrieve: checks a solution from a solution code

OTHER OPTIONS

–heuristic-iter: the number of iterations for the heuristic solver (default: 10000)

For example, to compute the contextuality degree of totally isotropic subspaces of dimension 1 (lines) for 2 qubits, run this command:

./qontextium --subspaces 1 2

Example files are provided in the misc folder, for example you can import a Peres-Mermin magic square with this command:

./qontextium --import assignment ./misc/qa_grid.txt

This command imports the same geometry, but using hypergrams:

./qontextium --import hypergram ./misc/grid.hypergraph.txt ./misc/grid.gram.txt

The following command applies the heuristic approach presented in MG24 and outputs in the file filename.txt a list of invalid lines forming a classical-embedded Cayley hexagon, as detailed in MG24. May be long, use CTRL+C to interrupt after ..

./qontextium --subspaces 1 3 --solver heuristic --export invalid > misc/filename.txt

The following command computes one of the results presented in SHKMGD23, namely the contextuality degree 24 of a complement of a skew embedding of a split Cayley hexagon. The last option removes interaction with the user after computation.

./qontextium --hexagon skew --complement --solver sat --no-interaction

Graph Visualization

There are multiple filters you can use to visualize the contextual graphs:

NOTHING

• This filter always returns false, meaning no lines will pass through this filter. It effectively filters out all lines.

ALL

• This filter always returns true, meaning all lines will pass through this filter.

POINT DEGREE

• This filter checks if any of the points in the geometry (for a given line) match a specific point degree specified by the user.

OBSERVABLE VALUE

• This filter checks if any of the points in the geometry for a line match a specific observable value given by the user.

LINE DEGREE

• This filter checks if the sorted degrees of the points in the geometry for each line exactly match the degrees specified by the user.

SYMMETRIC

• This filter checks if all points in the geometry for a line are symmetric. An observable is symmetric if the number of Y’s is even.

References

[MSGDH23]	Muller, Axel and Saniga, Metod and Giorgetti, Alain and de Boutray, Henri and Holweck, Frédéric. Revealing contextuality of quantum configurations with a SAT solver. Journées nationales du GDR GPL (Génie de la Programmation et du Logiciel), CNRS, groupe de travail LVP (Langages et Vérification de Programmes), 5-8 juin 2023, Rennes, France. Session posters et démos, 6 juin 2023. Poster
[MSGDH24]	Muller, Axel and Saniga, Metod and Giorgetti, Alain and de Boutray, Henri and Holweck, Frédéric. New and improved bounds on the contextuality degree of multi-qubit configurations. Mathematical Structures in Computer Science, 2024. Article
[MSGHK24]	Muller, Axel and Saniga, Metod and Giorgetti, Alain and Holweck, Frédéric and Kelleher, Colm. A new heuristic approach for contextuality degree estimates and its four- to six-qubit portrayals. Article
[MG24]	Muller, Axel and Giorgetti, Alain. An abstract structure determines the contextuality degree of observable-based Kochen-Specker proofs. Article
[SHKMGD23]	Saniga, Metod and Holweck, Frédéric and Kelleher, Colm and Muller, Axel and Giorgetti, Alain and de Boutray, Henri. Classically-embedded split Cayley hexagons rule three-qubit contextuality with three-element contexts. Article