212962^{1296} Exponentially Complex Quantum Many-Body Simulation via Scalable Deep Learning Method

For decades, people are developing efficient numerical methods for solving the challenging quantum many-body problem, whose Hilbert space grows exponentially with the size of the problem. However, this journey is far from over, as previous methods all have serious limitations. The recently developed deep learning methods provide a very promising new route to solve the long-standing quantum many-body problems. We report that a deep learning based simulation protocol can achieve the solution with state-of-the-art precision in the Hilbert space as large as $2^{1296}$ for spin system and $3^{144}$ for fermion system , using a HPC-AI hybrid framework on the new Sunway supercomputer. With highly scalability up to 40 million heterogeneous cores, our applications have measured 94% weak scaling efficiency and 72% strong scaling efficiency. The accomplishment of this work opens the door to simulate spin models and Fermion models on unprecedented lattice size with extreme high precision.Comment: Massive ground state optimizations of CNN-based wave-functions for $J1$-$J2$ model and $t$-$J$ model carried out on a heterogeneous cores supercompute

Emergent Schr\"{o}dinger cat states during superradiant phase transitions

Superradiant phase transitions (SPTs) are important for understanding light-matter interactions at the quantum level [1, 2], and play a central role in criticality-enhanced quantum sensing [3]. So far, SPTs have been observed in driven-dissipative systems [4-9], but the emergent light fields did not show any nonclassical characteristic due to the presence of strong dissipation. Here we report an experimental demonstration of the SPT featuring the emergence of a highly nonclassical photonic field, realized with a resonator coupled to a superconducting qubit, implementing the quantum Rabi model [10, 11]. We fully characterize the light-matter state by Wigner matrix tomography. The measured matrix elements exhibit quantum interference intrinsic of a photonic Schr\"{o}dinger cat state [12], and reveal light-matter entanglement. Besides their fundamental importance, these hitherto unobserved emergent quantum phenomena are useful for quantum metrology and fault-tolerant quantum computation.Comment: 19 pages, 14 figures, 2 table

Quantum simulation of topological zero modes on a 41-qubit superconducting processor

Quantum simulation of different exotic topological phases of quantum matter on a noisy intermediate-scale quantum (NISQ) processor is attracting growing interest. Here, we develop a one-dimensional 43-qubit superconducting quantum processor, named as Chuang-tzu, to simulate and characterize emergent topological states. By engineering diagonal Aubry-Andr$\acute{\mathrm{e}}$-Harper (AAH) models, we experimentally demonstrate the Hofstadter butterfly energy spectrum. Using Floquet engineering, we verify the existence of the topological zero modes in the commensurate off-diagonal AAH models, which have never been experimentally realized before. Remarkably, the qubit number over 40 in our quantum processor is large enough to capture the substantial topological features of a quantum system from its complex band structure, including Dirac points, the energy gap's closing, the difference between even and odd number of sites, and the distinction between edge and bulk states. Our results establish a versatile hybrid quantum simulation approach to exploring quantum topological systems in the NISQ era.Comment: Main text: 6 pages, 4 figures; Supplementary: 16 pages, 14 figure

Social Network Big Data Hierarchical High-Quality Node Mining

Compared with the conventional network data analysis, the data analysis based on social network has a very clear object of analysis, various forms of analysis, and more methods and contents of analysis. If the conventional analysis methods are applied to social network data analysis, we will find that the analysis results do not reach our expected results. The results of the above studies are usually based on statistical methods and machine learning methods, but some systems use other methods, such as self-organizing self-learning mechanisms and concept retrieval. With regard to the current data analysis methods, data models, and social network data, this paper conducts a series of researches from data acquisition, data cleaning and processing, data model application and optimization of the model in the process of application, and how the formed data analysis results can be used for managers to make decisions. In this paper, the number of customer evaluations, the time of evaluation, the frequency of evaluation, and the score of evaluation are clustered and analyzed, and finally, the results obtained by the two clustering methods applied in the analysis process are compared to build a customer grading system. The analysis results can be used to maintain the current Amazon purchase customers in a hierarchical manner, and the most valuable customers need to be given key attention, combining social network big data with micro marketing to improve Amazon’s sales performance and influence, developing from the original single shopping mall model to a comprehensive e-commerce platform, and cultivating their own customer base

Association Analysis of Private Information in Distributed Social Networks Based on Big Data

As people’s awareness of the issue of privacy leakage continues to increase, and the demand for privacy protection continues to increase, there is an urgent need for some effective methods or means to achieve the purpose of protecting privacy. So far, there have been many achievements in the research of location-based privacy services, and it can effectively protect the location privacy of users. However, there are few research results that require privacy protection, and the privacy protection system needs to be improved. Aiming at the shortcomings of traditional differential privacy protection, this paper designs a differential privacy protection mechanism based on interactive social networks. Under this mechanism, we have proved that it meets the protection conditions of differential privacy and prevents the leakage of private information with the greatest possibility. In this paper, we establish a network evolution game model, in which users only play games with connected users. Then, based on the game model, a dynamic equation is derived to express the trend of the proportion of users adopting privacy protection settings in the network over time, and the impact of the benefit-cost ratio on the evolutionarily stable state is analyzed. A real data set is used to verify the feasibility of the model. Experimental results show that the model can effectively describe the dynamic evolution of social network users’ privacy protection behaviors. This model can help social platforms design effective security services and incentive mechanisms, encourage users to adopt privacy protection settings, and promote the deployment of privacy protection mechanisms in the network

Full-Coupled Convolutional Transformer for Surface-Based Duct Refractivity Inversion

A surface-based duct (SBD) is an abnormal atmospheric structure with a low probability of occurrence buta strong ability to trap electromagnetic waves. However, the existing research is based on the assumption that the range direction of the surface duct is homogeneous, which will lead to low productivity and large errors when applied in a real-marine environment. To alleviate these issues, we propose a framework for the inversion of inhomogeneous SBD M-profile based on a full-coupled convolutional Transformer (FCCT) deep learning network. We first designed a one-dimensional residual dilated causal convolution autoencoder to extract the feature representations from a high-dimension range direction inhomogeneous M-profile. Second, to improve efficiency and precision, we proposed a full-coupled convolutional Transformer (FCCT) that incorporated dilated causal convolutional layers to gain exponentially receptive field growth of the M-profile and help Transformer-like models improve the receptive field of each range direction inhomogeneous SBD M-profile information. We tested our proposed method performance on two sets of simulated sea clutter power data where the inversion of the simulated data reached 96.99% and 97.69%, which outperformed the existing baseline methods

Entanglement-interference complementarity and experimental demonstration in a superconducting circuit

Abstract Quantum entanglement between an interfering particle and a detector for acquiring the which-path information plays a central role for enforcing Bohr’s complementarity principle. However, the quantitative relation between this entanglement and the fringe visibility remains untouched upon for an initial mixed state. Here we find an equality for quantifying this relation. Our equality characterizes how well the interference pattern can be preserved when an interfering particle, initially carrying a definite amount of coherence, is entangled, to a certain degree, with a which-path detector. This equality provides a connection between entanglement and interference in the unified framework of coherence, revealing the quantitative entanglement-interference complementarity. We experimentally demonstrate this relation with a superconducting circuit, where a resonator serves as a which-path detector for an interfering qubit. The measured fringe visibility of the qubit’s Ramsey signal and the qubit-resonator entanglement exhibit a complementary relation, in well agreement with the theoretical prediction