Quantum Reduced-Order Modeling via Variational Quantum SVD and Linear-Layer-Enhanced Quantum LSTM

Abstract. This paper proposes a hybrid quantum–classical reduced-order modeling (ROM) framework for unsteady fluid flows. It is based on variational quantum singular value decomposition (VQSVD) and a linear-layer enhanced quantum long short-term memory network (L-QLSTM). The proposed architecture first applies VQSVD to compress high-dimensional flow fields into a low-dimensional latent representation parameterized by reduced coefficients. The temporal fluid dynamics evolution of these coefficients is then learnt using L-QLSTM, which maps past coefficients to the next-step coefficients through variational quantum circuits with entangling layers and linear projections. The convergence of VQSVD under finite-shot stochastic gradients induced by parameter-shift measurements is analyzed. Furthermore, Lipschitz stability for L-QLSTM is established, and a multistep inference error bound accounting for VQSVD noise and model approximation is obtained. Finally, the predicted coefficients are lifted back to the full state space using the VQSVD modes. Two Numerical experiments: flow past a cylinder and flow past two cylinders demonstrate that the proposed quantum ROM achieves faster convergence and improved long-horizon stability compared with the classical ROM. Reproducibility of computational results. This paper has been awarded the “SIAM Reproducibility Badge: Code and data available” as a recognition that the authors have followed reproducibility principles valued by SISC and the scientific computing community. Code and data that allow readers to reproduce the results in this paper are available at https://github.com/EdeIgard/QROM_VQSVD-LQLSTM and in the supplementary materials ( QROM_VQSVD-LQLSTM-main.zip [90.7MB]). [Formula: see text]