An-encoding-perspective-for-quantum-classification-advantage-using-NISQ-algorithms

This repository contains the notebooks and data used for the paper "An encoding perspective for quantum classification advantage using NISQ algorithms" published on arXiv By Mancilla J. and Pere C., 2022.

Content

• Notebooks
• Libraries
• Datasets
• Results

Notebooks

9 notebooks were made for this study. The objective is to clearly separate each approach and allowing the reader to have all the information for one specific dataset with one specific encoding approach. One notebook called Baselines_ML was done to generate the machine learning models baseline.

List: - Baselines_ML.ipynb: contains the results of the application of Logistic Regression (LR), Decision Tree (CART), k-Neireast Neighbours (KNN), Gaussian Naïve Bayes (NB), and Support Vector Machine (SVM) on the UCI_Credit_Card.csv and fraud_detection_bank_dataset.csv datasets. - LDA_ML_QML_UCI_Credit_Card.ipynb: LDA dimensionality reduction applied on the UCI_Credit_Card.csv data - PCA_ML_QML_UCI_Credit_Card.ipynb: PCA dimensionality reduction applied on the UCI_Credit_Card.csv data - SKPP_ML_QML_UCI_Credit_Card.ipynb: SKPP dimensionality reduction applied on the UCI_Credit_Card.csv data - SVD_ML_QML_UCI_Credit_Card.ipynb: SVD dimensionality reduction applied on the UCI_Credit_Card.csv data - LDA_ML_QML_fraud_bank.ipynb: LDA dimensionality reduction applied on the fraud_detection_bank_dataset.csv data - PCA_ML_QML_fraud_bank.ipynb: PCA dimensionality reduction applied on the fraud_detection_bank_dataset.csv data - SKPP_ML_QML_fraud_bank.ipynb: SKPP dimensionality reduction applied on the fraud_detection_bank_dataset.csv data - SVD_ML_QML_fraud_bank.ipynb: SVD dimensionality reduction applied on the fraud_detection_bank_dataset.csv data

Libraries

For this study we used scikit-learn (sklearn) for classical machine learning models and Pennylane for the VQA classifier. The quantum kernel used for the QSVC is imported from Qiskit. The cross_validate and train_test_spli functions were also imported from sklearn.

• LR, CART, KNN, NB, and SVM are implemented with sklearn
• QSVC is the SVC algorithm provided by sklearn using a quantum kernel available with Qiskit.
• VQC is implemented with Pennylane

Datasets

We used two datasets: UCI Credit Card fraud and a Fraud bank dataset. This choice was made to be close to the real-world where datasets have a lot of features.

Results

Below you will find the main results of the paper.

UCI Credit Card

Baseline

| Algorithm | Precision | Recall | f1-score | Matthews | Balanced | | :---: | :---: | :---: | :---: | :---: | :---: | | - | (%) | (%) | (%) | corcorref (%) | Accuracy (%) | | LR | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | -0.22 (0.44) | 49.99 (0.01) | | KNN | 38.74 (2.03) | 15.45 (1.51) | 22.07 (1.76) | 12.43 (0.76) | 54.26 (0.65) | | CART | 37.79 (1.51) | 40.53 (1.51) | 39.10 (1.34) | 20.99 (1.45) | 60.76 (0.75) | | NB | 24.71 (0.89) | 88.41 (1.55) | 38.62 (1.15) | 11.94 (1.74) | 55.82 (0.88) | | SVM | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 50.00 (0.00) |

Quantum

| Algorithm | Precision | Recall | f1-score | Matthews | Balanced | | :---: | :---: | :---: | :---: | :---: | :---: | | - | (%) | (%) | (%) | corcorref (%) | Accuracy (%) | | QSVC (SVD) | 20.00 (40.00) | 2.21 (4.82) | 3.92 (8.45) | 5.98 (12.30) | 51.10 (2.41) | | VQA (SVD) | 77.50 | 26.72 | 39.74 | 19.75 | 58.00 | | QSVC (PCA) | 12.00 (29.93) | 1.06 (2.14) | 1.88 (3.84) | 0.51 (8.04) | 49.93 (1.30) | | VQA (PCA) | 88.10 | 25.87 | 40.00 | 18.95 | 58.55 |
| QSVC (SKPP) | 0.0 (0.0) | 0.0 (0.0) | 0.0 (0.0) | 0.0 (0.0) | 50.0 (0.0) | | VQA (SKPP) | 25.58 | 27.5 | 26.51 | 7.3 | 53.75 | | QSVC (LDA) | 67.02 (13.31) | 33.44 (10.08) | 43.96 (10.97) | 38.51 (10.97) | 64.6 (5.08) | | VQA (LDA) | 41.30 | 100.00 | 58.46 | 59.28 | 92.54 |

Fraud bank

Baseline

| Algorithm | Precision | Recall | f1-score | Matthews | Balanced | | :---: | :---: | :---: | :---: | :---: | :---: | | - | (%) | (%) | (%) | corcorref (%) | Accuracy (%) | | LR | 71.54 (2.77) | 47.27 (1.96) | 56.88 (1.62) | 46.89 (1.88) | 70.2 (0.88) \ | KNN | 74.34 (1.77)| 64.56 (2.36) | 69.09 (1.91) | 59.16 (2.65) | 78.22 (1.39) \ | CART | 80.68 (1.87) | 81.69 (2.06) | 81.17 (1.63) | 74.27 (2.25) | 87.28 (1.21) \ | NB | 28.43 (1.07) | 96.95 (0.88) | 43.96 (1.3) | 12.58 (1.36) | 54.07 (0.54) \ | SVM | 0.0 (0.0) | 0.0 (0.0) | 0.0 (0.0) | 0.0 (0.0) | 50.0 (0.0) \

Quantum

| Algorithm | Precision | Recall | f1-score | Matthews | Balanced | | :---: | :---: | :---: | :---: | :---: | :---: | | - | (%) | (%) | (%) | corcorref (%) | Accuracy (%) | | QSVC (SVD) | 85.02 (11.42) | 39.24 (8.53) | 52.94 (8.19) | 49.55 (7.54) | 68.45 (3.97) | | VQA (SVD) | 62.50 | 72.22 | 60.61 | 26.57 | 74.09 | | QSVC (PCA) | 0.0 (0.0) | 0.0 (0.0) | 0.0 (0.0) | 0.0 (0.0) | 50.0 (0.0)| | VQA (PCA) | 67.39 | 25.41 | 36.90 | 7.16 | 53.09 | | QSVC (SKPP) | 56.28 (11.17) | 46.46 (7.21) | 50.3 (6.8) | 35.53 (8.7) | 66.65 (4.02)|
| VQA (SKPP) | 89.86 | 68.89 | 77.99 | 70.67 | 82.60 | | QSVC (LDA) | 82.35 (10.29) | 65.92 (8.79) | 2.93 (8.14) | 66.35 (9.9) | 80.67 (4.94)| | VQA (LDA) | 84.00 | 84.44 | 75.68 | 55.81 | 83.92 |