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arXiv:2402.06415 · Communications Physics

Many-body computing on Field Programmable Gate Arrays

Songtai Lv, Yang Liang, Yuchen Meng, Xiaochen Yao, Jincheng Xu, Yang Liu, Qibin Zheng, Haiyuan Zou

Published Mar 25, 2025• 4 citations
arXivHTMLPDF

Abstract

Abstract A new implementation of many-body calculations is of paramount importance in the field of computational physics. In this study, we leverage the capabilities of Field Programmable Gate Arrays (FPGAs) for conducting quantum many-body calculations. Through the design of appropriate schemes for Monte Carlo and tensor network methods, we effectively utilize the parallel processing capabilities provided by FPGAs. This has resulted in a remarkable tenfold speedup compared to CPU-based computation for a Monte Carlo algorithm. We also demonstrate, for the first time, the utilization of FPGA to accelerate a typical tensor network algorithm. Our findings unambiguously highlight the significant advantages of hardware implementation and pave the way for novel approaches to many-body calculations.

DOI
10.1038/s42005-025-02050-z

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Abstract A new implementation of many-body calculations is of paramount importance in the field of computational physics. In this study, we leverage the capabilities of Field Programmable Gate Arrays (FPGAs) for conducting quantum many-body calculations. Through the design of appropriate schemes for Monte Carlo and tensor network methods, we effectively utilize the parallel processing capabilities provided by FPGAs. This has resulted in a remarkable tenfold speedup compared to CPU-based computation for a Monte Carlo algorithm. We also demonstrate, for the first time, the utilization of FPGA to accelerate a typical tensor network algorithm. Our findings unambiguously highlight the significant advantages of hardware implementation and pave the way for novel approaches to many-body calculations.
Increasing the degree of freedom for quantum entanglement within tensor networks can enhance the depiction of the essence in many-body systems. However, this enhancement comes with a significant increase in computational complexity and critical slowing down, which drastically increases time consumption. This work converts a quantum tensor network algorithm into a classical circuit on the Field Programmable Gate Arrays (FPGAs) and arranges the computing unit with a dense parallel design, efficiently optimizing the time consumption. Test results show that the FPGA-based design achieves a computational speed 1.7 times greater than that of the central processing unit and is comparable to the graphics processing unit. This work explores a scalable and reusable approach suitable for parallel tensor operations implemented on FPGA, advancing research in quantum physics for many-body computing and quantum technologies.
Improving the computational efficiency of quantum many-body calculations from a hardware perspective remains a critical challenge. Although field-programmable gate arrays (FPGAs) have recently been exploited to improve the computational scaling of algorithms such as Monte Carlo methods, their application to tensor network algorithms is still at an early stage. In this work, we propose a fine-grained parallel tensor network design based on FPGAs to substantially enhance the computational efficiency of two representative tensor network algorithms: the infinite time-evolving block decimation (iTEBD) and the higher-order tensor renormalization group (HOTRG). By employing a quad-tile partitioning strategy to decompose tensor elements and map them onto hardware circuits, our approach effectively translates algorithmic computational complexity into scalable hardware resource utilization, enabling an extremely high degree of parallelism on FPGAs. Compared with conventional CPU-based implementations, our scheme exhibits superior scalability in computation time, reducing the bond-dimension scaling of the computational cost from O(Db3)O(D_b^3)O(Db3​) to O(Db)O(D_b)O(Db​) for iTEBD and from O(Db6)O(D_b^6)O(Db6​) to O(Db2)O(D_b^2)O(Db2​) for HOTRG. This work provides a theoretical foundation for future hardware implementations of large-scale tensor network computations.
We present the first application of field programmable gate arrays (FPGAs) as new, customizable hardware architectures that can be harnessed for the fast and energy-efficient calculation of quantum dynamics simulations of large chemical/material systems. Instead of tailoring the software to fixed hardware (which is the typical case for writing quantum chemistry code for CPUs/GPUs), FPGAs allow us to directly customize the underlying hardware - even at the level of specific electrical signals in the circuit - to give a truly optimized computational performance for complex quantum dynamics calculations. By offloading the most intensive and repetitive calculations onto an FPGA, we show that the computational performance of our hardware implementation for real-time electron dynamics calculations can even exceed that of optimized commercial mathematical libraries running on high-performance GPUs. In addition to this impressive computational speedup, we show that FPGAs are immensely energy-efficient and consume 4 times less energy than modern GPU or CPU architectures. These energy savings are a practical and important metric for supercomputing centers (several of which exceed over $1 million in power costs alone), as exascale computing capabilities become more widespread and commonplace. Taken together, the implementation techniques and performance metrics of our study demonstrate that FPGAs could play a promising role in upcoming quantum chemistry and materials science applications, particularly for the acceleration and energy-efficient execution of quantum dynamics calculations.
We present the first application of field programmable gate arrays (FPGAs) as new, customizable hardware architectures for carrying out fast and energy-efficient quantum dynamics simulations of large chemical/material systems. Instead of tailoring the software to fixed hardware, which is the typical case for writing quantum chemistry code for central processing units (CPUs) and graphics processing units (GPUs), FPGAs allow us to directly customize the underlying hardware (even at the level of specific electrical signals in the circuit) to give a truly optimized computational performance for quantum dynamics calculations. By offloading the most intensive and repetitive calculations onto an FPGA, we show that the computational performance of our real-time electron dynamics calculations can even exceed that of optimized commercial mathematical libraries running on high-performance GPUs. In addition to this impressive computational speedup, we show that FPGAs are immensely energy-efficient and consume 4 times less energy than modern GPU or CPU architectures. These energy savings are a practical and important metric for supercomputing centers (many of which exceed over $1 million in power costs alone), as exascale computing capabilities become more widespread and commonplace. Taken together, the implementation techniques and performance metrics of our study demonstrate that FPGAs could play a promising role in upcoming quantum chemistry and materials science applications, particularly for the acceleration and energy-efficient execution of quantum dynamics calculations.
Tensor Networks (TNs) are a computational framework traditionally used to model quantum many-body systems. Recent research has demonstrated that TNs can also be effectively applied to Machine Learning (ML) tasks, producing results comparable to conventional supervised learning methods. In this work, we investigate the use of Tree Tensor Networks (TTNs) for high-frequency real-time applications by harnessing the low-latency capabilities of Field-Programmable Gate Arrays (FPGAs). We present the implementation of TTN classifiers on FPGA hardware, optimized for performing inference on classical ML benchmarking datasets. Various degrees of parallelization are explored to evaluate the trade-offs between resource utilization and algorithm latency. By deploying these TTNs on a hardware accelerator and utilizing an FPGA integrated into a server, we fully offload the TTN inference process, demonstrating the system’s viability for real-time ML applications.
Recent technological advances have led to a number of emerging platforms such as multi-cores, reconfigurable computing, and graphics processing units. We present a comparative study of multi-cores, field-programmable gate arrays, and graphics processing units for a Quantum Monte Carlo chemistry application. The speedups of these implementations are measured relative to a multi-core implementation and the accuracy of each implementation compared against the double-precision CPU implementation. The Brook+ AMD implementation shows the best overall speedup and accuracy, with the mixed-precision NVIDIA CUDA implementation outperforming the Brook+ implementation for larger atomic clusters with a slightly lower accuracy than the Brook+ and FPGA implementations. KeywordsQuantum Monte Carlo, Field-Programmable Gate Arrays, Multi-core processors, Graphics Processing Units.