Quantum Three-Coloring Graphs Iteritavely: Repository contains open source code for comparing qutrits against qubits for solving graph three-colouring using the Quantum Approximate Optimization Algorithm (QAOA).

import pennylane as qml
import qtcorgi
import networkx as nx

edge_list = [[0,1]] # Edge list using numbered nodes
graph = nx.Graph(edge_list)
qutrit_solver = qtcorgi.QutritQaoa(graph)

@qml.qnode(qml.device("default.qutrit", 2))
def circuit(gamma, beta):
    qutrit_solver.unitary_circuit([gamma],[beta],1)
    return qml.expval(qml.GellMann(0,3))

>>> qml.draw(circuit)(1,2)
0: ──TH─╭●───────────────────────────╭●─────TRX(2.00)──TRX(2.00)──TRX(2.00)─┤  <GellMann(3)>
1: ──TH─╰TAdd†──TRZ(1.33)──TRZ(1.33)─╰TAdd──TRX(2.00)──TRX(2.00)──TRX(2.00)─┤    

This project consists of two packages described bellow:

qaoa3colouring acts as a graph 3-colouring solver using either qubit and qutrit based QAOA.

qaoa3colouring also allows for comparison by entering data into plot builders.

experiments allows a user to recreate the data and figures used in IEEE submission. It also allows for users to update hyper-parameters and sets of graphs that are considered.

This will be updated to include all future paper submissions.

To solve a graph using the qaoa3colouring package users will create a QuditQaoa object for each graph that the user plans to solve. The user will then call QuditQaoa.qaoa_3_colouring() method to solve the graph.

The QuditQaoa object will either be from the QubitQaoa or QutritQaoa class. This selection determines if a simulation using qubits or qutrits will be used.

Currently, NumberOfGates and ProbabilityCorrectSampled classes can be used to make figures based on saved data.

import networkx as nx
import qtcorgi
edge_list = [[0,1], [1,2], [2,0]] # Edge list using numbered nodes
graph = nx.Graph(edge_list)
qutrit_solver = qtcorgi.QutritQaoa(graph, samples=10)
solution_values = qutrit_solver.qaoa_3_colouring()

>>> print("Final objective value:", solution_values[0])
Final objective value: -1.977612038050443
>>> print("Sampled_solutions as ints:", solution_values[1])
Sampled_solutions as ints: [15 21 21 11 21 19  7  7  5 19]
>>> print("Trit-sting array:", solution_values[2])
Trit-sting array: [1 2 0][2 1 0][2 1 0][1 0 2][2 1 0][2 0 1][0 2 1][0 2 1][0 1 2][2 0 1]
>>> print("Most frequently sampled trit-stings:", solution_values[3])
Most frequently sampled trit-stings: 210
>>> print("Input parameters:", solution_values[4])
Input parameters: [[ 0.3113133   0.396807    0.52144379]
                   [-0.41018815 -0.14562269 -0.28965116]]

To repeat a paper and change hyperparameters the experiments package can be used. By simply calling experiments.replicate_IEEE_paper() the experiment will be repeated and the graphs will be saved. default configurations used for the IEEE paper are found in experiments/config_IEEE

Configuration parameters are listed and described bellow:

• save_location (str): location to save the data folder.
• save_folder_name (str): data folder name.
• num_layers: number of QAOA layers used to differing graph sizes.
• num_qutrit_steps: maximal number of optimization steps for qutrits.
• num_qubit_steps: maximal number of optimization steps for qubits.
• num_samples: number of samples taken for solution.
• learning_rate: optimization learning rate.
• fourth_colour_cost: cost for fourth colour for qubit cost Hamiltonian.
• qubit_convergence_value: convergence value for qubit optimization halting.
• graphs_to_generate_dictionary: dictionary describing which graphs to generate and solve.
• n_for_layers: number of nodes for graphs used to test variable number of layers.
• test_layers: list of number of layers being tested.
• opt_connectivity_labels: labels for the connectivity of tested graphs.
• cost_connectivity_labels: labels for the connectivity of graphs used for cost metrics.
• graphs_count_gates_dictionary: dictionary describing which graphs to generate and find circuit cost metrics.
• min_qubit_steps: minimum number of optimization steps done for qubit optimization.
• fig_width: width of final figure.
• fig_height: height of final figure.
• fig_save_folder: folder where figure is saved.
• use_separate_params_qubit: boolean deciding if the colouring cost parameter and the fourth colour cost parameter are seperated.
• connectivity_colours: list of colours used in figures.
• opt_bar_width : width of bars on plotted graph.
• cost_bar_width : width of bars on plotted graph.

The only supported OS for this repo is Linux Currently, the Pennylane tested branch is missing some of the necessary features for this package to work. To be able to run this branch it is necessary to install the dev branch which can be done using the following command:

pip install git+https://github.com/PennyLaneAI/pennylane.git

To run this branch it is also necessary to install JAX, it is recommended to use GPU acceleration. This requires an nvidia graphics card with updated nvidia drivers installed. It also requires CUDA, which can be difficult to install. Detailed installation instructions for JAX and CUDA can be found at JAX's GitHub page. However, if CUDA is not previously installed it is recommended to install both using the following commands:

pip install --upgrade pip

# CUDA 12 installation
pip install --upgrade "jax[cuda12_pip]" -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html

If your GPU doesn't support CUDA 12 replace "cuda12_pip" with "cuda11_pip".

Finally installing the project can be done by the following command:

pip install -e /PATH/TO/REPO