Quantum automorphism groups for graphs

Library for quantum automorphism groups of graphs

This library relies on SageMath software system.

The main program file is quant_aut_group_func.py. The recommended way to use it is through the jupyterlab interface, launched from the Sage desktop application. This way the python interpreter should have access to Sage without further configuration. Place quant_aut_group_func.py to the working directory of jupyterlab. In the jupyterlab, use Launcher to open a Python 3 console, then import the program and run it by evaluating compute function with the graph as input.

Here is a sample interaction:

[1]: import quant_aut_group_func
[2]: from sage.graphs.graph_generators import graphs
[3]: quant_aut_group_func.compute(graphs.CycleGraph(5))
We are working with Cycle graph
There are 13 orbits in the triple product of vertices.
There are 63 orbits in the quadruple product of vertices.
The script is not run as main, we resort to single-core computation.
We now have rank 63, spanned by 204 elements, in the 4-box space.
We found enough elements in the 4-box space to conclude that the quantum automorphism groups is classical.
[4]: quant_aut_group_func.compute(graphs.CompleteGraph(3))
We are working with Complete graph
There are 5 orbits in the triple product of vertices.
There are 14 orbits in the quadruple product of vertices.
The script is not run as main, we resort to single-core computation.
We now have rank 14, spanned by 204 elements, in the 4-box space.
We found enough elements in the 4-box space to conclude that the quantum automorphism groups is classical.
	

There is a variant, quant_aut_group_scpt.py, meant to be run as a script. This allows parallel computation through multiprocessing package.

$ /path/to/python3 quant_aut_group_scpt.py
We are working with Orthogonal Polar Graph O^-(6, 2).
There are 3 orbits in the product of vertices.
There are 15 orbits in the triple product of vertices.
There are 116 orbits in the quadruple product of vertices.
We now have rank 116, spanned by 204 elements, in the 4-box space.
We found enough elements in the 4-box space to conclude that the quantum automorphism groups is classical.
	

Again the python executable needs to have access to Sage library. To get a correct path, run

import sys
print(sys.executable)
	

in the python console launched from jupyterlab.