| One of the major challenges in condensed matter physics is to understand the mi-cro pairing mechanism of unconventional superconductivity.Since the discovery of cuprates and iron-based superconductors,there is a lot of theoretical and experimental research on this topic.However,the pairing mechanism of unconventional supercon-ductivity have not reached a consensus.These two families ofunconventional supercon-ductors share some similarities in the phase diagram,electronic structure,magnetism and so on.To uniformly understand the pairing mechanism of unconventional supercon-ductivity based on these similarities can help to find and design new high-temperature superconductors.In turn,if the proposed new superconductors are verified by exper-iments,which can help us to understand in depth the micro-mechanism of unconven-tional superconductivity.In the first part of this thesis,we predict hexagonal CaFe2As2 may be unconventional superconductor under the assumption that there should be one unified superconducting mechanism for these two families of unconventional supercon-ductors.We investigate the electronic and magnetic structures of the 122(AM2B2)hexag-onal transition-metal pnictides with A=(Sr,Ca),M=(Cr,Mn,Fe,Co,Ni)and B=(As,P,Sb).It is found that the family of materials shares critical similarities with those of tetragonal structures that include the famous iron-based high-temperature superconduc-tors.In both families,the next nearest neighbor(NNN)effective antiferromagnetic(AFM)exchange couplings reach the maximum value in the iron-based materials.While the NNN couplings in the latter are known to be responsible for the C-type AFM state and to result in the extended s-wave superconducting state upon doping,they cause the former to be extremely frustrated magnetic systems and can lead to a time reversal symmetry broken d + id superconducting state upon doping.The iron-based compounds with the hexagonal structure,thus if synthesized,can help us to determine the origin of high-temperature superconductivityIn recent years,machine learning,especially deep learning triggered intensive re-search in academia and extensive applications in the industrial community.As a branch of machine learning,deep learning,which is based on the high capacity of deep neural networks,performs well in many real-world applications,such as image recognition and generation,natural language processing and so on.Depend on whether there are labels in the data set,machine learning algorithms can be roughly divided into super-vised learning algorithms and unsupervised learning algorithms.Supervised learning is to learn a map from the input to output vector or learn a conditional probability dis-tribution.However unsupervised learning is to model the joint probability distribution.Unsupervised generative models find wide applications in complex tasks beyond clas-sification and regression,such as generating new samples and density estimation.The major difficulty with generative modeling is the high dimensionality of the random vari-ables being modeled,which brings a computational challenge.In the second part of this thesis,we try to scale up the generative model by quantum computation.Quantum mechanics is inherently probabilistic in light of Born's rule.Using quan-tum circuits as probabilistic generative models for classical data exploits their superior expressibility and eff-icient direct sampling ability.However,training of quantum cir-cuits can be more challenging compared to classical neural networks due to lack of efficient differentiable learning algorithm.We devise an adversarial quantum-classical hybrid training scheme via coupling a quantum circuit generator and a classical neural network discriminator together.We numerically simulate the learning of generative ad-versarial quantum circuit using the prototypical Bars-and-Stripes dataset.Generative adversarial quantum circuits is a fresh approach to machine learning which may enjoy the practically useful quantum advantage on near-term quantum devices. |
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