Solving quantum many-body problems is one of the most fascinating research fields in condensed matter physics. An efficient numerical method is crucial to understand the mechanism of novel physics, such as the high Tc superconductivity, as one has to find the optimal solution in the exponentially large Hilbert space. The development of Artificial Intelligence (AI) provides a unique opportunity to solve the quantum many-body problems, but there is still a large gap from the goal. In this work, we present a novel computational framework, and adapt it to the Sunway supercomputer. With highly efficient scalability up to 40 million heterogeneous cores, we can drastically increase the number of variational parameters, which greatly improves the accuracy of the solutions. The investigations of the spin-1/2 J1-J2 model and the t-J model achieve unprecedented accuracy and time-to-solution far beyond the previous state of the art.
Solving quantum many-body problems is one of the most fascinating research fields in condensed matter physics. An efficient numerical method is crucial to understand the mechanism of novel physics, such as the high Tc superconductivity, as one has to find the optimal solution in the exponentially large Hilbert space. The development of Artificial Intelligence (AI) provides a unique opportunity to solve the quantum many-body problems, but there is still a large gap from the goal. In this work, we present a novel computational framework, and adapt it to the Sunway supercomputer. With highly efficient scalability up to 40 million heterogeneous cores, we can drastically increase the number of variational parameters, which greatly improves the accuracy of the solutions. The investigations of the spin-1/2 J1-J2 model and the t-J model achieve unprecedented accuracy and time-to-solution far beyond the previous state of the art.
Abstract The quantum many-body problems are important for condensed matter physics, however solving the problems are challenging because the Hilbert space grows exponentially with the size of the problem. The recently developed deep learning methods provide a promising new route to solve long-standing quantum many-body problems. We report that a deep learning based simulation can achieve solutions with competitive precision for the spin J 1 – J 2 model and fermionic t-J model, on rectangular lattices within periodic boundary conditions. The optimizations of the deep neural networks are performed on the heterogeneous platforms, such as the new generation Sunway supercomputer and the multi graphical-processing-unit clusters. Both high scalability and high performance are achieved within an AI-HPC hybrid framework. The accomplishment of this work opens the door to simulate spin and fermionic lattice models with state-of-the-art lattice size and precision.
The simulation of quantum matter with classical hardware plays a central role in the discovery and development of quantum many-body systems, with far-reaching implications in condensed matter physics and quantum technologies. In general, efficient and sophisticated algorithms are required to overcome the severe challenge posed by the exponential scaling of the Hilbert space of quantum systems. In contrast, hardware built with quantum bits of information are inherently capable of efficiently finding solutions of quantum many-body problems. While a universal and scalable quantum computer is still beyond the horizon, recent advances in qubit manufacturing and coherent control of synthetic quantum matter are leading to a new generation of intermediate scale quantum hardware. \n \nThe complexity underlying quantum many-body systems closely resembles the one encountered in many problems in the world of information and technology. In both contexts, the complexity stems from a large number of interacting degrees of freedom. A powerful strategy in the latter scenario is machine learning, a subfield of artificial intelligence where large amounts of data are used to extract relevant features and patterns. In particular, artificial neural networks have been demonstrated to be capable of discovering low-dimensional representations of complex objects from high-dimensional dataset, leading to the profound technological revolution we all witness in our daily life. \n \nIn this Thesis, we envision a new paradigm for scientific discovery in quantum physics. On the one hand, we have the essentially unlimited data generated with the increasing amount of highly controllable quantum hardware. On the other hand, we have a set of powerful algorithms that efficiently capture non-trivial correlations from high-dimensional data. Therefore, we fully embrace this data-driven approach to quantum mechanics, and anticipate new exciting possibilities in the field of quantum many-body physics and quantum information science. We revive a powerful stochastic neural network called a restricted Boltzmann machine, which slowly moved out of fashion after playing a central role in the machine learning revolution of the early 2010s. We introduce a neural-network representation of quantum states based on this generative model. We propose a set of algorithms to reconstruct unknown quantum states from measurement data and numerically demonstrate their potential, with important implications for current experiments. These include the reconstruction of experimentally inaccessible properties, such as entanglement, and diagnostics to determine sources of noise. Furthermore, we introduce a machine learning framework for quantum error correction, where a neural network learns the best decoding strategy directly from data. We expect that the full integration between quantum hardware and artificial intelligence will become the gold standard, and will drive the world into the era of fault-tolerant quantum computing and large-scale quantum simulations.
Artificial intelligence has become a transformative technology for predictive modelling across scientific, industrial, financial, and healthcare applications. However, the increasing complexity of large-scale datasets, high-dimensional feature spaces, and computationally intensive learning algorithms has exposed significant limitations in conventional computing architectures. Recent developments in quantum computing and high-performance computing have created unprecedented opportunities to accelerate artificial intelligence by improving computational efficiency, optimization capability, and predictive accuracy. This paper presents a comprehensive study of a quantum-driven artificial intelligence framework that integrates quantum algorithms with high-performance computing infrastructure to enhance predictive modelling performance. The proposed framework combines quantum-enhanced optimization, parallel heterogeneous computing, distributed data processing, and hybrid machine learning architectures to address computational bottlenecks encountered in conventional predictive systems. The study reviews recent developments in quantum artificial intelligence, evaluates emerging computational paradigms, identifies current research challenges, and proposes a scalable architecture suitable for future intelligent decision-support systems. The findings demonstrate that integrating quantum computation with high-performance computing can significantly improve prediction quality, optimization efficiency, scalability, and computational sustainability across diverse application domains while establishing a foundation for next-generation intelligent computing environments.
This thesis focuses on the development, application, and high-performance implementation of numerical methods for simulating quantum many-body systems. In the first chapter, I provide an overview of several most successful conventional approaches for simulating quantum many-body systems, along with their current limitations. Then, the basic properties of the quantum spin model, which will be the subject of study in the following chapters, and its ground state are briefly summarized. Additionally, I discuss the background and the motivations of the research projects carried out during my PhD research. Chapter 2 introduces two numerical algorithms that are extensively used in this thesis, which are exact diagonalization (ED) and variational Monte Carlo. I outline the process of constructing a Hamiltonian matrix and employing iterative methods for exact diagonalization. Subsequently, I introduce the mechanism of the four important components in the ``standard" variational Monte Carlo that are widely used in the most recent research. In Chapter 3, we propose a symmetry-projected variational ansatz in the form of linear combinations of simple restricted Boltzmann machines. This construction allows one to explore states outside of the original variational manifold and increase the representation power with moderate computational effort. Besides allowing one to restore spatial symmetries, an expansion in terms of Krylov states using a Lanczos recursion offers a solution that can further improve the quantum state accuracy. We illustrate these ideas with an application to the Heisenberg J1−J2 model on the square lattice, a paradigmatic problem under debate in condensed matter physics,and achieve state-of-the-art accuracy in the representation of the ground state. In Chapter 4, we present a variational approach based on a Chebyshev expansion of the spectral function, and each Chebyshev polynomial is represented by a neural network quantum state. The Chebyshev moments are obtained by recursively applying the Hamiltonian and projecting on the space of variational states using a modified natural gradient descent method. We compare this approach with a modified approximation of the spectral function which uses a Krylov subspace constructed from the "Chebyshev wave functions." We present results for the one-dimensional and two-dimensional Heisenberg models on the square lattice and compare them with those obtained by other methods in the literature. In Chapter 5, we describe a method to carry out thermodynamic simulations of quantum many-body models using typicality and variational representations of quantum states. Minimally entangled typical thermal states (METTS) are a construction that allows one to solve for the imaginary time evolution of quantum many-body systems. By using wave functions that are weakly entangled, one can take advantage of efficient representations in the form of matrixproduct states. We generalize these ideas to arbitrary variational wave functions and we focus, as an illustration, on the particular case of restricted Boltzmann machines. We demonstrate the application of the method to quantum spin systems in one and two spatial dimensions. In Chapter 6, we study the properties of the impurity band in heavily doped nonmagnetic semiconductors using the Jacobi-Davidson algorithm and the supervised deep learning method. The disorder averaged inverse participation ratio and Thouless number calculation show us the rich structure inside the impurity band. A convolutional neural network model, which is trained to distinguish the extended/localized phase of the Anderson model with high accuracy, shows us the results in good agreement with the conventional approach. Together, we find that there are three mobility edges in the impurity band for a specific on-site impurity potential, which means the presence of the extended states while filling the impurity band. In the final chapter, Chapter 7, we discuss the implementation of architecture-aware optimizations for spin dynamics simulations on x86 CPUs and Nvidia GPUs. The time cost of evaluating the spin-spin correlation functions in real space increases quadratically as the number of spins N, leading to significant computational effort, making the simulation of large spin systems very challenging. We propose to use a highly optimized general matrix multiply (GEMM) subroutine to calculate the dynamical spin-spin correlation function that can achieve near-optimal hardware utilization. Furthermore, we fuse the element-wise operations in the calculation of S(q,t) into the in-house GEMM kernel to reduce memory latency. On Nvidia GPU, we perform the on-the-fly calculation in the epilogue of the GEMM subroutine to avoid saving intermediate results on global memory, which significantly reduces memory usage and achieves better performance than cuBLAS.--Author's abstract
The intersection of artificial intelligence (AI) and quantum mechanics represents a frontier of scientific exploration, offering the potential to revolutionize our understanding of quantum systems. Despite the promise, significant challenges remain in effectively integrating AI techniques within quantum mechanics frameworks. This study aims to investigate the applications of AI in quantum mechanics, identifying both the challenges and opportunities presented by this interdisciplinary approach. The focus is on understanding how AI can enhance quantum simulations, optimize computations, and improve experimental designs. A comprehensive literature review was conducted, analyzing recent advancements in AI algorithms applied to quantum mechanics. Case studies were examined to illustrate successful implementations and the limitations encountered. Key metrics for evaluation included computational efficiency, accuracy, and scalability. Findings indicate that AI techniques, particularly machine learning and neural networks, can significantly expedite quantum simulations and enhance predictive accuracy. However, challenges such as data sparsity, interpretability of AI models, and the integration of AI with quantum algorithms were identified as significant barriers to progress. This research highlights the transformative potential of AI in advancing quantum mechanics while acknowledging the inherent challenges. Addressing these challenges will require collaborative efforts across disciplines, paving the way for innovative solutions that leverage AI to deepen our understanding of quantum phenomena and improve technological applications.
Artificial Intelligence (AI) and quantum computing are converging to form a new era of ultra-fast computational problem-solving. Quantum optimization algorithms—when integrated with AI-driven heuristics, reinforcement learning, and neural-guided search models—offer unprecedented capabilities for tackling complex problems such as NP-hard optimization, logistics scheduling, cryptographic analysis, and large-scale simulation tasks. This research investigates the combined potential of AI-augmented quantum algorithms, focusing on how machine learning enhances qubit efficiency, error mitigation, quantum annealing performance, and adaptive gate-level optimization. A practical case study evaluates hybrid AI-quantum models applied to combinatorial optimization tasks, demonstrating significant reductions in computational time and improved solution accuracy. Findings highlight a future in which AI-enhanced quantum systems redefine computation, enabling breakthroughs in science, industry, and national innovation systems