Vectorized Symmetric and Fermionic Tensor Network Implementations for GPU-Accelerated Variational Monte Carlo
Abstract
Variational Monte Carlo (VMC) calculations based on tensor networks (TN) have recently achieved competitive accuracy in ground-state calculations of strongly correlated spin and fermionic systems. However, existing tensor network VMC (TN-VMC) algorithms have not been formulated in a manner that can fully utilize GPU acceleration. We tackle the key missing ingredient, namely, the vectorized evaluation of tensor network amplitudes and tensor network operations. This ensures high GPU utilization by batching over computations with identical structure. In particular, we show how to achieve vectorization for the practically relevant case of abelian symmetric tensor networks (which includes fermionic tensor networks) by developing a ``flat'' tensor network formalism for block-sparse tensor representation and contraction. Using this, we construct a GPU-adapted symmetric TN-VMC workflow with batched tensor network computation. In the two-dimensional Fermi--Hubbard model, we demonstrate a GPU speedup of up to 300 × over single core CPU implementations, for fermionic TN variational wavefunctions.
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BibTeX
@misc{du2026vectorized,
title = {{Vectorized Symmetric and Fermionic Tensor Network Implementations for GPU-Accelerated Variational Monte Carlo}},
author = {Si-Jing Du and Johnnie Gray and Ao Chen and Garnet Kin-Lic Chan},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27861},
eprint = {2608.27861},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27861},
}
RIS
TY - UNPB
TI - Vectorized Symmetric and Fermionic Tensor Network Implementations for GPU-Accelerated Variational Monte Carlo
AU - Si-Jing Du
AU - Johnnie Gray
AU - Ao Chen
AU - Garnet Kin-Lic Chan
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.27861
UR - https://arxiv.org/abs/2608.27861
AB - Variational Monte Carlo (VMC) calculations based on tensor networks (TN) have recently achieved competitive accuracy in ground-state calculations of strongly correlated spin and fermionic systems. However, existing tensor network VMC (TN-VMC) algorithms have not been formulated in a manner that can fully utilize GPU acceleration. We tackle the key missing ingredient, namely, the vectorized evaluation of tensor network amplitudes and tensor network operations. This ensures high GPU utilization by batching over computations with identical structure. In particular, we show how to achieve vectorization for the practically relevant case of abelian symmetric tensor networks (which includes fermionic tensor networks) by developing a ``flat'' tensor network formalism for block-sparse tensor representation and contraction. Using this, we construct a GPU-adapted symmetric TN-VMC workflow with batched tensor network computation. In the two-dimensional Fermi--Hubbard model, we demonstrate a GPU speedup of up to 300 × over single core CPU implementations, for fermionic TN variational wavefunctions.
ER -