MicroCloud Hologram Inc., a technology service provider, proposed an innovative hardware acceleration technology that converts the quantum tensor network algorithm into parallel computing circuits that can run on field programmable gate arrays (FPGA), achieving efficient quantum spin model simulation on classical hardware. This achievement provides a brand-new engineered path for quantum physics research, quantum algorithm verification, and digital twin simulation of future quantum devices.
In the research of quantum many-body systems, the tensor network (TN) algorithm is an extremely efficient numerical tool. It overcomes the problem of exponential state space expansion to a certain extent by decomposing high-dimensional quantum states into a network structure of multiple low-dimensional tensors. Typical tensor network models include matrix product states (MPS), projected entangled pair states (PEPS), and multi-scale entanglement renormalization (MERA), etc. These algorithms play a foundational role in condensed matter physics, quantum phase transitions, quantum spin model simulations, and other aspects.
However, when we hope to improve the precision of system characterization and introduce higher entanglement degrees of freedom, the dimensions and connectivity of tensors grow sharply, causing the computational complexity to rapidly cross from polynomial to exponential levels. Taking a two-dimensional spin system as an example, when the entanglement rank expands from χ=8 to χ=32, the floating-point operations per iteration increase nearly a hundredfold, and storage bandwidth and memory access latency become bottlenecks. This exponential explosion characteristic makes it difficult even for high-end CPU and GPU platforms to complete simulation tasks within a reasonable time.
To this end, HOLO attempts to break out of the limitations of traditional processor architectures and explore feasible paths for algorithm reconstruction and logic mapping at the hardware level. Field programmable gate arrays (FPGA), with their reconfigurability, parallelism, and low-latency characteristics, provide new possibilities for tensor network computations. By directly mapping core computational modules (such as tensor contraction, tensor unfolding, matrix multiplication-addition operations, etc.) into hardware circuits at the logic level, it can greatly reduce memory access consumption and control overhead, achieving deep pipelined high-density parallel computing.
The core of HOLO's technology lies in algorithm-hardware co-design, which dissects the tensor network algorithm from the software logic level into computational units that can be directly hardware-ized, and builds a high-density parallel scalable architecture with FPGA as the carrier.
First, a systematic analysis was performed on the tensor network structure of quantum spin models. Typical systems represented by the Heisenberg spin chain and the two-dimensional Ising model have their Hamiltonians decomposable into local interaction terms, encoded into several local tensors through tensor networks. The contraction of each tensor node essentially corresponds to tensor product, matrix multiplication, and summation operations. Traditional CPU computations rely on sequential execution of general instruction sets, while GPUs, although possessing large-scale parallelism, are limited by memory access latency and kernel scheduling, making it difficult to achieve targeted optimization. The FPGA architecture allows direct definition of these computational logics at the hardware level, eliminating redundant scheduling links, enabling data to flow continuously in a pipeline manner in the on-chip high-speed cache.
In the implementation, HOLO constructed a Hierarchical Tensor Contraction Pipeline. This pipeline includes three main levels:
Input and scheduling layer: responsible for decomposing high-dimensional tensors into several manageable block structures, and performing data flow scheduling and dependency analysis.
Core computing layer: composed of multiple MAC Array, supporting tensor contraction operations of arbitrary dimensions. Each computing unit adopts customized logic to achieve pipeline-level parallelism for floating-point addition and multiplication.
Output and reduction layer: executes the merging, normalization, and intermediate state caching of tensor results, providing input for subsequent iterations.
In the hardware logic design, through the combined method of Verilog and high-level synthesis (HLS) tools, tensor operation circuits are automatically generated, and multi-partition strategies are adopted for different tensor connectivity graphs. Through static scheduling and data reuse mechanisms, the computing units form a high-density parallel array on-chip, achieving the maximum computational throughput rate under limited logic resources.
This technology takes FPGA as the core hardware platform, proposing and implementing a parallelized hardware architecture for accelerating quantum tensor network computations. Through algorithm structure reconstruction, logic circuit mapping, pipelined design, and mixed-precision optimization, HOLO successfully transforms complex tensor network computational tasks into efficient FPGA logic operations, achieving a performance breakthrough that is 1.7 times faster than CPU and with energy efficiency improved by more than 2 times. This technology not only demonstrates the potential of FPGA in quantum simulation but also provides practical basis for quantum algorithm hardware implementation and reconfigurable quantum accelerator design.
In the future, HOLO will continue along the design philosophy from algorithm to circuit, promoting the hardware implementation of more quantum computing core modules, including quantum variational algorithms (VQE), quantum linear system solvers (QLSA), and FPGA-ization of quantum machine learning models, to build a complete quantum algorithm acceleration ecosystem. It is believed that, through continuous research in this direction, FPGA will become an important bridge between quantum computing and classical computing, providing solid technical support for the industrialization development of quantum technology.
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