Tensor Ring Parametrized Variational Quantum Circuits for Large Scale Quantum Machine Learning

Quantum Machine Learning (QML) is an emerging research area advocating the use of quantum computing for advancement in machine learning. Since the discovery of the capability of Parametrized Variational Quantum Circuits (VQC) to replace Artificial Neural Networks, they have been widely adopted to different tasks in Quantum Machine Learning. However, despite their potential to outperform neural networks, VQCs are limited to small scale applications given the challenges in scalability of quantum circuits. To address this shortcoming, we propose an algorithm that compresses the quantum state within the circuit using a tensor ring representation. Using the input qubit state in the tensor ring representation, single qubit gates maintain the tensor ring representation. However, the same is not true for two qubit gates in general, where an approximation is used to have the output as a tensor ring representation. Using this approximation, the storage and computational time increases linearly in the number of qubits and number of layers, as compared to the exponential increase with exact simulation algorithms. This approximation is used to implement the tensor ring VQC. The training of the parameters of tensor ring VQC is performed using a gradient descent based algorithm, where efficient approaches for backpropagation are used. The proposed approach is evaluated on two datasets: Iris and MNIST for the classification task to show the improved accuracy using more number of qubits. We achieve a test accuracy of 83.33\% on Iris dataset and 79.57\% and 74.08\% on binary and ternary classification of MNIST dataset using a 4 qubit circuit. A test accuracy of 90.01\% with binary classification and 76.31\% with ternary classification is obtained on MNIST data using an 8 qubit circuit. These results outperform the results on VQCs implemented on Qiskit, and being scalable, demonstrates the potential for VQCs to be used for large scale Quantum Machine Learning applications.