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Review of Scientific Instruments

FPGA acceleration of tensor network computing for quantum spin models

Yang Liang, Songtai Lv, Zhiping Tang, Liguo Zhou, Qibin Zheng, Haiyuan Zou

Published Jan 1, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1063/5.0239473

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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.
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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.
Most research in quantum computing today is performed against simulations of quantum computers rather than true quantum computers. Simulating a quantum computer entails implementing all of the unitary operators corresponding to the quantum gates as tensors. For high numbers of qubits, performing tensor multiplications for these simulations becomes quite expensive, since NNN-qubit gates correspond to 2N2^{N}2N-dimensional tensors. One way to accelerate such a simulation is to use field programmable gate array (FPGA) hardware to efficiently compute the matrix multiplications. Though FPGAs can efficiently perform tensor multiplications, they are memory bound, having relatively small block random access memory. One way to potentially reduce the memory footprint of a quantum computing system is to represent it as a tensor network; tensor networks are a formalism for representing compositions of tensors wherein economical tensor contractions are readily identified. Thus we explore tensor networks as a means to reducing the memory footprint of quantum computing systems and broadly accelerating simulations of such systems.
Field Programmable Gate Arrays (FPGAs) have been used in most of the physics sub-fields for various unique purposes. This includes particle physics, quantum optics, and, more recently, quantum computing. FPGAs boast many benefits over previous experimental and computational setups. They are versatile, easy to program, and cost-effective, leading to an understandable desire to incorporate them into the new field of quantum computing. While FPGAs have been used to help control the readout and control of physical qubits, they can also be a good tool for improving algorithm simulations, which is the focus of this paper. Different algorithms have different computational limits because of the varying operations and circuit depth levels. Due to the ease of incorporating parallel processes and the ability to optimize FPGAs on a deeper level, we can speed up computationally expensive operations, increasing the size of the quantum circuits we can simulate. This paper aims to provide an educational walkthrough for quantum computing physicists interested in taking advantage of FPGAs in their research. Our findings indicate that an inexpensive FPGA with a clock rate of 100MHz can perform simple, unoptimized matrix operations on the order of 107 ns faster than a CPU using optimized Python libraries. This can be further improved upon using more expensive hardware and optimized designs. This will provide many researchers and students with the tools needed to study quantum algorithms without the need for costly hardware.
Many large-scale optimisation problems, such as those in power systems, finance and logistics can be potentially solved in the fundamentally new approach of quantum algorithms, namely Quantum Approximate Optimisation Algorithm (QAOA). In the context of fuzzy systems for instance, it is already shown that some of the intense computation associated with complex or higher-order fuzzy logic systems can be offloaded to such quantum algorithms. While the quantum computation hardware technology is still in its infancy, efficient simulations of the quantum algorithms play a crucial role in advancing quantum algorithms. The current CPU/GPU-based approaches suffer from high energy consumption and speed and scalability limitations. This paper presents the current position of our research to develop an efficient and scalable QAOA simulation based on a large network of Field-Programmable Gate Array (FPGA) modules, inspired by FPGA’s hardware-level parallelism. Although there exist a few attempts on using FPGA for general quantum circuits simulation, this project introduces a novel approach by employing a highly efficient recursive matrix decomposition algorithms specifically designed for QAOA. This work can pave the pathway a scalable and energy-efficient solution for cross-domain optimisation problems. The actual results and evaluations are to be reported in follow-up publications.
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.