Modern heterogeneous high-performance computing (HPC) systems powered by advanced graphics processing unit (GPU) architectures enable accelerating computing with unprecedented performance and scalability. Here, we present a GPU-accelerated solver for the three-dimensional (3D) time-dependent Dirac equation optimized for distributed HPC systems. The solver named GaDE is designed to simulate the electron dynamics in atoms induced by electromagnetic fields in the relativistic regime. It combines MPI with CUDA/HIP to target both NVIDIA and AMD GPU architectures. We discuss our implementation strategies in which most of the computations are carried out on GPUs, taking advantage of the GPU-aware MPI feature to optimize communication performance. We evaluate GaDE on the pre-exascale supercomputer LUMI, powered by AMD MI250X GPUs and HPE's Slingshot interconnect. Single-GPU performance on NVIDIA A100, GH200, and AMD MI250X shows comparable performance between A100 and MI250X in compute and memory bandwidth, with GH200 delivering higher performance. Weak scaling on LUMI demonstrates exceptional scalability, achieving 85% parallel efficiency across 2048 GPUs, while strong scaling delivers a 16x speedup on 32 GPUs - 50% efficiency for a communication-intensive, time-dependent Dirac equation solver. These results demonstrate GaDE's high scalability, making it suitable for exascale systems and enabling predictive simulations for ultra-intense laser experiments probing relativistic quantum effects.
Modern heterogeneous high-performance computing (HPC) systems powered by advanced graphics processing unit (GPU) architectures enable accelerating computing with unprecedented performance and scalability. Here, we present a GPU-accelerated solver for the three-dimensional (3D) time-dependent Dirac equation optimized for distributed HPC systems. The solver named GaDE is designed to simulate the electron dynamics in atoms induced by electromagnetic fields in the relativistic regime. It combines MPI with CUDA/HIP to target both NVIDIA and AMD GPU architectures. We discuss our implementation strategies in which most of the computations are carried out on GPUs, taking advantage of the GPU-aware MPI feature to optimize communication performance. We evaluate GaDE on the pre-exascale supercomputer LUMI, powered by AMD MI250X GPUs and HPE's Slingshot interconnect. Single-GPU performance on NVIDIA A100, GH200, and AMD MI250X shows comparable performance between A100 and MI250X in compute and memory bandwidth, with GH200 delivering higher performance. Weak scaling on LUMI demonstrates exceptional scalability, achieving 85% parallel efficiency across 2048 GPUs, while strong scaling delivers a 16x speedup on 32 GPUs - 50% efficiency for a communication-intensive, time-dependent Dirac equation solver. These results demonstrate GaDE's high scalability, making it suitable for exascale systems and enabling predictive simulations for ultra-intense laser experiments probing relativistic quantum effects.
An algorithm is presented for the coupled-cluster singles, doubles, and perturbative triples correction [CCSD(T)] method based on the density fitting or the resolution-of-the-identity (RI) approximation for performing calculations on heterogeneous computing platforms composed of multicore CPUs and graphics processing units (GPUs). The directive-based approach to GPU offloading offered by the OpenMP application programming interface has been employed to adapt the most compute-intensive terms in the RI-CCSD amplitude equations with computational costs scaling as O ( N O 2 N V 4 ), O ( N O 3 N V 3 ), and O ( N O 4 N V 2 ) (where N O and N V denote the numbers of correlated occupied and virtual orbitals, respectively) and the perturbative triples correction to execute on GPU architectures. The pertinent tensor contractions are performed using an accelerated math library such as cuBLAS or hipBLAS. Optimal strategies are discussed for splitting large data arrays into tiles to fit them into the relatively small memory space of the GPUs, while also minimizing the low-bandwidth CPU–GPU data transfers. The performance of the hybrid CPU–GPU RI-CCSD(T) code is demonstrated on pre-exascale supercomputers composed of heterogeneous nodes equipped with NVIDIA Tesla V100 and A100 GPUs and on the world’s first exascale supercomputer named “Frontier”, the nodes of which consist of AMD MI250X GPUs. Speedups within the range 4–8× relative to the recently reported CPU-only algorithm are obtained for the GPU-offloaded terms in the RI-CCSD amplitude equations. Applications to polycyclic aromatic hydrocarbons containing 16–66 carbon atoms demonstrate that the acceleration of the hybrid CPU–GPU code for the perturbative triples correction relative to the CPU-only code increases with the molecule size, attaining a speedup of 5.7× for the largest circumovalene molecule (C 66 H 20 ). The GPU-offloaded code enables the computation of the perturbative triples correction for the C 60 molecule using the cc-pVDZ/aug-cc-pVTZ-RI basis sets in 7 min on Frontier when using 12,288 AMD GPUs with a parallel efficiency of 83.1%.
As is intrinsic to the fundamental goal of quantum computing, classical simulation of quantum algorithms is notoriously demanding in resource requirements. Nonetheless, simulation is critical to the success of the field and a requirement for algorithm development and validation, as well as hardware design. GPU-acceleration has become standard practice for simulation, and due to the exponential scaling inherent in classical methods, multi-GPU simulation can be required to achieve representative system sizes. In this case, inter-GPU communications can bottleneck performance. In this work, we present the introduction of MPI into the QED-C Application-Oriented Benchmarks to facilitate benchmarking on HPC systems. We review the advances in interconnect technology and the APIs for multi-GPU communication. We benchmark using a variety of interconnect paths, including the recent NVIDIA Grace Blackwell NVL72 architecture that represents the first product to expand high-bandwidth GPU-specialized interconnects across multiple nodes. We show that while improvements to GPU architecture have led to speedups of over 4.5X across the last few generations of GPUs, advances in interconnect performance have had a larger impact with over 16X performance improvements in time to solution for multi-GPU simulations.
Efficient scalable implementations are presented for two single-reference coupled-cluster (CC) methods with non-iterative corrections for triple excitations, which accurately describe single bond dissociations in molecules in contrast to the standard CCSD(T) approach. These methods are (a) the completely renormalized coupled-cluster theory, CR-CC(2,3), and (b) the ΛCCSD(T) approach, the triples energy corrections in both of which are formulated using the left eigenvector of the CC similarity transformed Hamiltonian. The density fitting approximation is employed for factorizing the two-electron repulsion integrals (ERIs), which eliminates memory bottlenecks associated with the storage of the four-index ERIs by allowing an integral-direct algorithm. Massively parallel algorithms have been developed for the above methods within the GAMESS quantum chemistry program using a hybrid MPI and OpenMP based parallelization model. All compute-intensive steps in the CCSD amplitude and the left eigenvector equations, as well as the triples corrections in both methods, have been adapted to execute on graphical processing units (GPUs) using the OpenMP target directives. Performance of these codes is demonstrated on petascale supercomputers equipped with NVIDIA A100 GPUs. While the CR-CC(2,3) and ΛCCSD(T) computations take roughly twice as much time as the standard CCSD(T) method, the GPU-offloaded codes are shown to impart 3.5-5× accelerations relative to the CPU-only parallel codes, thereby significantly reducing the time-to-solution for the CR-CC(2,3) and ΛCCSD(T) methods.
Quantum computing simulation on a classical computer is difficult due to the exponential runtime and memory overhead. Previous work addresses the difficulty by utilizing multiple Graphical Processing Units (GPUs) and multi-node computers. GPUs are efficient for handling runtime issues but have limited total accessible memory space. Meanwhile, the memory of a multi-node computer can be scaled to the petabytes order, but its bandwidth for access from host computers (CPUs) is narrow. To simultaneously accelerate simulation and enlarge the total memory space, we propose a heterogeneous parallelization approach by combining GPUs and CPUs. Our simulator allocates memory to the GPUs first, and then to the CPUs. It thus accelerates simulation by using the full capabilities of the GPUs if memory for the simulation fits in the GPUs on a cluster. Allocating memory to the CPUs reduces benefits of the GPUs but enlarges the capacity of qubits in the simulation. In such case, it can exploit the memory of the GPUs to add one more qubit in the simulation if the size of memory in a node is the power of two (such as 512GB). We show empirical performance evaluations of our simulator in a distributed environment of POWER9.
The drastic growth of data generation by companies such as Google and Facebook, the widespread integration of IoT devices into everyday life, advancements in artificial intelligence, and the rise of social media platforms are driving a shift from model-driven to data-driven science. This surge in data created a need for massively parallel accelerators such as graphics processing units (GPU). High Performance Computing (HPC) are required to accommodate the growing complexity of data-driven technologies. HPC demands are anticipated to reach exascale levels within this decade. Since 2004, three waves of high-performance accelerators have driven advancements in HPC: the first wave introduced Central Processing Units (CPUs) and Field Programmable Gate Arrays (FPGAs), the second wave brought General Purpose Graphics Processing Units (GPGPUs), and the third wave focused on machine learning specific GPUs. Recent research reveals that quantum processing units (QPUs) have the potential to be the fourth wave of high-performance acceleration in the near future. However, as Quantum Computing is still in its early stages, its practical and useful quantum computation is yet to be developed. In this paper, a heterogeneous CPU-GPU-QPU (HCGQ) accelerator is proposed. The accelerator is based on an input size threshold, where the CPU assigns smaller input sizes workloads to the GPU, and larger input sizes to the QPU. This dynamic workload allocation is realized entirely through software-level integration. Using the searching algorithm and deep neural networks as benchmarks, it was observed that the HCGQ accelerator outperformed standalone GPUs and QPUs in terms of speed and energy efficiency.
We present a GPU-accelerated software package for the evaluation of analytic two-electron energy and gradient contributions in Hartree-Fock (HF) and Density Functional theory (DFT) calculations. The implementation is provided as a Python library with a C++ backend, enabling straightforward integration into modern computational chemistry and drug-discovery workflows. The code supports single-point energy and nuclear gradient evaluations on both single- and multi-GPU systems, and employs MPI-based parallelization with dynamic load balancing in multi-node environments. We report comprehensive benchmarks demonstrating favorable scaling with respect to system size, as well as high throughput for batched evaluations relevant to molecular dynamics, geometry optimization, and large-scale virtual screening. Parallel execution of a single system was carried out on up to 24 A100 GPUs. The implementation builds on optimized GPU-enabled variants of the LibintX and GauXC libraries to efficiently compute density-fitted Coulomb, semi-numerical exchange, and exchange--correlation contributions.