Classifying Many-Body Wavefunctions by Means of a Quantum Convolutional Neural Network

We aim to use Quantum Machine Learning by attempting to classify quantum mechanical data. The goal is to train a Quantum Convolutional Neural Network (QCNN) to detect the zero temperature quantum phases, in particular the quantum critical point, of the Transverse Field Ising model (TFIM), an archetypal quantum many-body system. This approach allows us to investigate whether a QCNN can be used as a classifier for quantum phase transitions. The TFIM is solved by the Variational Quantum Eigensolver (VQE). The VQE is a quantum algorithm that uses the variational method to find close approximations to the ground state of the corresponding system. The outcome of the VQE is a set of datapoints, represented as quantum circuits, which can be used as input data for the QCNN with the intent of correctly labeling the phase of the system. The promising results of this study allowed us to display the effectiveness of the QCNN as a quantum classifier. We find that the accuracy of our model proves to be consistently high, demonstrating the future potential that Quantum Machine Learning offers as a quantum classifier. Larger, more complex systems, such as the Periodic Anderson model and the Hubbard model, will become the next targets of interest.