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Machine learning has been applied on a wide variety of models, from classicalstatistical mechanics to quantum strongly correlated systems for theidentification of phase transitions. The recently proposed quantumconvolutional neural network (QCNN) provides a new framework for using quantumcircuits instead of classical neural networks as the backbone of classificationmethods. We present here the results from training the QCNN by thewavefunctions of the variational quantum eigensolver for the one-dimensionaltransverse field Ising model (TFIM). We demonstrate that the QCNN identifieswavefunctions which correspond to the paramagnetic phase and the ferromagneticphase of the TFIM with good accuracy. The QCNN can be trained to predict thecorresponding phase of wavefunctions around the putative quantum criticalpoint, even though it is trained by wavefunctions far away from it. Thisprovides a basis for exploiting the QCNN to identify the quantum criticalpoint.

An Application of Quantum Machine Learning on Quantum Correlated  Systems: Quantum Convolutional Neural Network as a Classifier for Many-Body  Wavefunctions from the Quantum Variational Eigensolver