Fraud Detection

Binary classification of genuine vs fraudulent credit card transactions using classical-quantum hybrid model.

Code

This code is a Keras-Pennylane implementation of the "Supervised quantum neural networks" proposed in "Continuous-variable quantum neural networks". https://arxiv.org/pdf/1806.06871v1.pdf The original implementation using Strawberry Fields and Tensorflow is found here. https://github.com/XanaduAI/quantum-neural-networks/blob/master/fraud_detection/fraud_detection.py Thanks to Pennylane Tensorflow plug-in, we can easily convert quantum circuits into Keras layers and use Keras's built in loss and optimizer functions.

Dataset

The original dataset is a record of 284,806 genuine and fraudulent credit card transactions. Each transaction is respresented by 29 features. The modifications to the original data are:

• The truncated dataset contains 1,968 samples: 492 faudulent and 1,476 sampled genuine transactions. The ratio is balanced to 1:3.
• The 29 features are ordered based on Principal Component Analysis, hece the paper suggests selecting only 10.
• The resulting csv file in the folder contains 1,968 samples with 10 features and label.

Architecture

The proposed classical-quantum hybrid model had two hidden layers, outputs a vector of length 14, encodes it in quantum state using various quantum gates, performs quantum computation using quantum layers.

I am using the mean square error, which is not true to the cost function of the paper. It is due to the fact Pennylane does not support state vector extraction yet.

Qauntum state encoding

As per Schuld's paper "Supervised quantum machine learning models are kernel methods", quantum ML model can be viewed as a kernel method, a way of mapping data into a higher dimensional Hilbert space. https://arxiv.org/pdf/2101.11020.pdf Then what sets an algorithm apart is the classical data encoding into quantum states. One way of encoding is using the entries of each vector as parameters of available quantum gates. Photonic qunatum computing provides a rich way to encode data with its linear and nonlinear gates:

• Squeezing gate
• Interferometer (composed of beam splitter and rotation gates)
• Displacement gate
• Kerr gate

Dataflow

• Prepare data using Pandas, Scikit-learn, and convert to Tensorflow tensors. One-hot encoding is used for labels.
• Define classical layers
  • 2 hidden layers with 10 neurons
  • output layer with 14 neurons
• Encode the output of the classical layers in quantum state using the output of the classical layer as the parameters of quantum gates.
• Define quantum layers (initialize the parameters to be optimized)
• Create a Pennylane quantum circuit. The measurement returns a 2-dimensional vector to match the one-hot encoded labels.
• Create a hybrid Keras model (Pennylane plug-in converts the quantum layers as Keras layers)
• Train using Keras loss function and optimizer

The paper suggests cutoff dimension 10. That would be a better approximation of the overall resulting quantum state. However the cutoff dimension of only 2 is giving a good result as well. Experimenting with different cutoff dimension is encouraged.