VQSplines and GVQSplines

This repository contains the code to reproduce the results presented in the research work titled 'Variational Quantum Splines - Moving Beyond Linearity for Quantum Activation Functions'.

Description

The first part of work starts with the aim to reformulate in a Variational fashion the QSPlines work present in the paper Quantum Splines for Non-Linear Approximations in order to move from a fault-tolerant model to a NISQ one. In the second part a new methodology is proposed, in order to tackle the same problem in a more generalized way and overcome many limitations of the previous works.

As explained in the paper 4 function are studied, sigmoid, rectified linear unit (relu), exponential linear unit (elu) and the sin function.

Repository sructure

• experiments: folder containing the notebook to reproduce the experiments.
  • experiment_GQS.ipynb: file used to train and evaluate a GQSpline model. It can be used to reproduce the best performing GQSpline models for each target function.
  • experiment_VQS.ipynb: file used to train and evaluate a VQSpline model. It can be used to reproduce the best performing VQSpline models for each target function.
• results: folder containing the results of the experiment as dataframe in json format.
• plots: folder containing the plots of the models for each function.
• run_gqsplines.py: script to perform and save multiple experiments (GQSpline).
• run_vqsplines.py: script to perform and save multiple experiments (VQSpline).
• vqls.py: file containing the implementation of the VQLS and the Quantum inner product.
• vqspline_v2.py: scrtipt used to train the model (VQSpline).
• gqspline_v2.py: scrtipt used to train the model (GQSpline).
• utils.py: collection of utility functions.

Launch multiple experiments GQSplines

Run the run_gqsplines.py script with the fololowing command line paramters

• -sp name of the saving file and path (NOTE the results will be saved with json formatting)
• -mi maximum number of iteration for the COBYLA optimizator
• -en number of experiments to launch
• -func name of the function to approximate, canbe choosen between sigmoid tanh, elu,relu, and sin.
• -nq number of qubits
• -h outputs list of possible parameters

Running the script without any parameter is the same as running:

python run_gqsplines.py -sp results.json -mi 300 -en 25 -func sigmoid -nq 3

The saved file is a Dataset containing the following features:

• Condition number float
• norm(yk) float
• training_cost list[float]
• exe_time float (seconds)
• in_train_weight list[list[float]]
• RSS_q float
• RSS_h float
• seed int

Launch multiple experiments VQSplines

Run the run_vqsplines.py script with the fololowing command line paramters

• -sp name of the saving file and path (NOTE the results will be saved with json formatting)
• -mi maximum number of iteration for the COBYLA optimizator
• -en number of experiments to launch
• -func name of the function to approximate, canbe choosen between sigmoid tanh, elu,relu, and sin.
• -stp number of knots
• -h outputs list of possible parameters

Running the script without any parameter is the same as running:

python run_gqsplines.py -sp results.json -mi 300 -en 25 -func sigmoid -stp 20

The saved file is a Dataset containing the following features:

• Condition number float
• norm(yk) float
• training_cost list[float]
• exe_time float (seconds)
• in_train_weight list[list[float]]
• RSS_q float
• RSS_h float
• seed int

Installation

To run the code and reproduce the results of the paper, it is recommended to re-create the same testing environment following the procedure below.

Note: it's assumed Anaconda is installed

• First clone the repository
• Second, create a conda environment from scratch and install the requirements specified in the requirements.txt file:

  # enter the repository
  cd project_folder
  
  # create an environment with desired dependencies found in the requirements.txt file
  conda env create
  pip install -r requirements.txt