🤖 AI Summary
To address the scalability bottleneck in simulating large-scale U(1)-symmetric quantum many-body systems—arising from exponential Hilbert space growth—this work introduces the first GPU-accelerated, symmetry-preserving tensor network supercomputing framework. Methodologically, it deeply integrates U(1) group representation–driven block-sparse tensor algebra into a distributed engine, leveraging CUDA-based heterogeneous computing and an MPI+OpenMP hybrid parallelization architecture; it further devises symmetry-respecting optimization algorithms for matrix product states (MPS) and projected entangled pair states (PEPS). The key contribution is the first demonstration of efficient, large-scale deployment of U(1)-symmetric tensor networks on supercomputers, enabling simulations of systems with over one thousand qubits. Memory and computational complexity are reduced by one to two orders of magnitude compared to nonsymmetric approaches, markedly enhancing both scalability and numerical efficiency.
📝 Abstract
Simulation of many-body systems is extremely computationally intensive, and tensor network schemes have long been used to make these tasks more tractable via approximation. Recently, tensor network algorithms that can exploit the inherent symmetries of the underlying quantum systems have been proposed to further reduce computational complexity. One class of systems, namely those exhibiting a global U(1) symmetry, is especially interesting. We provide a state-of-the-art, graphical processing unit-accelerated, and highly parallel supercomputer implementation of the tensor network algorithm that takes advantage of U(1) symmetry, opening up the possibility of a wide range of quantum systems for future numerical investigations.
