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The phase transitions of a series of Co-doped Heusler alloys, Ni2Mn1−xCoxGa (0⩽x⩽0.2), were investigated experimentally using the magnetization measurements, x-ray diffraction, and calorimetric measurements up to their respective melting points. With increasing Co concentration, the structural transition temperatures, Curie temperatures, and melting points, were observed to increase, while the order–disorder transition temperatures decreased. Temperature-dependent x-ray diffraction experiments revealed two different crystal structures in the low-temperature martensite phase for different Co concentrations. However, above their respective structural transitions, both low-temperature crystal structures transformed into the L21 cubic structure. These findings enabled the construction of a complete magnetic and structural phase diagram for Ni2Mn1−xCoxGa, spanning from cryogenic temperatures to the melting points. The temperature-dependent XRD results revealed the abrupt changes in interatomic Mn–Mn distances, which validates the crucial role of Mn–Mn interatomic distance and the effect of the magnetic coupling competition in the structural stability between the martensite phase and austenite phase. 

Machine learning has been applied to a wide variety of models, from classical statistical mechanics to quantum strongly correlated systems, for classifying phase transitions. The recently proposed quantum convolutional neural network (QCNN) provides a new framework for using quantum circuits instead of classical neural networks as the backbone of classification methods. We present the results from training the QCNN by the wavefunctions of the variational quantum eigensolver for the one-dimensional transverse field Ising model (TFIM). We demonstrate that the QCNN identifies wavefunctions corresponding to the paramagnetic and ferromagnetic phases of the TFIM with reasonable accuracy. The QCNN can be trained to predict the corresponding ‘phase’ of wavefunctions around the putative quantum critical point even though it is trained by wavefunctions far away. The paper provides a basis for exploiting the QCNN to identify the quantum critical point.