Quantum Neural Network architecture to perform Machine Learning tasks on NISQ computers

Abstract

Models known as quantum neural networks (QNNs) combine the benefits of quantum theory with those of neural networks. They are said to be more proficient in reaching the desired performance than classical models. But it is challenging to demonstrate this importance using a practically relevant problem on the current Noisy Intermediate Scale Quantum (NISQ) computers. This thesis aims to develop a QNN architecture that can be implemented on a real quantum device without significant changes in results due to errors. The limitations imposed on implementing QNNs are due to errors in NISQ computers that suffer from decoherence, gate errors, measurement errors, and cross-talk. To reduce the error introduced due to the high accumulation of gate errors and decoherence, a combination of small QNNs, Hierarchical bi-linear classification structure, and Clustering is used.

The architecture is tested for low-dimensional datasets (Iris flower species and Ripley's crab datasets) with results provided. An additional classification result for a high-dimensional dataset is provided. A standard QNN consists of an encoding circuit, parameterized quantum circuit (PQC), measurement operations, and cost function. The encoding circuit maps the classical data represented as a column vector to a quantum state. At the same time, PQC transforms the quantum state (or updates the position of the quantum state on the Bloch sphere) to obtain desired output state. The cost function is the fidelity between the QNN result and desired output subtracted from one. The parameters of PQC are updated repeatedly until the cost function is minimized, hence completing the learning process. The quantum state obtained from the QNN circuit is reconstructed by obtaining measurement results. The statistical distance data obtained from the final measurement is used to classify the data points into one of the main clusters. The sub-clusters present in these main clusters are identified with the help of more detailed analysis and QNN unit training. The final number of QNN units required to implement the classification problem depends on the dataset's selected features and target labels. Three IBM cloud devices are used to check the performance of the QNN units against the simulator results. The variation in the results due to QV and CLOPS is also observed. Small QNN units might be a desirable alternative for applications based on realistic QML simulations, but more study is required to boost performance. This is a modest step towards a noise-resilient quantum machine learning framework.