Nonlinear dynamics is ubiquitous in nature, ranging from chemical pattern formation to ocean circulation, yet its simulation on quantum computers is fundamentally limited by the unitary nature of quantum evolution. We propose the quantum Koopman method, a data-driven framework that embeds nonlinear dynamics into a learned linear representation and implements the resulting evolution using shallow quantum circuits.
arXiv:2607. 18552v1 Announce Type: cross Abstract: Quantum reservoir computing (QRC) uses the dynamics of a fixed or weakly tuned quantum system to transform temporal and sequential inputs into measured features, while training is typically confined to a classical readout.
By Shehbaz Tariq, Muhammad Talha, Arshid Ali, Muhammad Diyan, Symeon Chatzinotas
arXiv:2608. 00850v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a versatile approach for solving nonlinear partial differential equations (PDEs), yet achieving high accuracy efficiently using these techniques remains challenging for high-dimensional or multiscale systems.
By Fabio Pereira dos Santos, Renato Portugal, J\'ulio de Castro Vargas Fernandes, Lucas Timotheo Sanches
arXiv:2607. 21688v1 Announce Type: cross Abstract: Machine-learning surrogates of physical systems face a paradox: explainable models facing the challenge of expressivity to capture complex nonlinear flows, whereas expressive deep surrogates match high-fidelity simulations only through massive parameterisations that turn the learned dynamics into a black box.
By Xiao Xue, Maida Wang, Mingyang Gao, Minh Chung, Peter V. Coveney
arXiv:2604. 15645v2 Announce Type: replace Abstract: We present QPINNACLE, an open-source computational framework for physics-informed neural networks (PINNs) that integrates modern training strategies, multi-GPU acceleration, and hybrid quantum-classical architectures within a unified modular workflow.
By Ziv Chen, Hemanth Chandravamsi, Shimon Pisnoy, Aaron Goldgewert, Gal Shaviner, Boris Shragner, Steven H. Frankel
arXiv:2607. 00365v1 Announce Type: cross Abstract: Artificial intelligence (AI) and quantum information (QI) are rapidly co-evolving.
By Min Chen, Yu Gan, Xin Jin, Yuqing Li, Junqi Wang, Zeguan Wu, Yunfei Wang, Bingzhi Zhang, Priyam Srivastava, Tianlong Chen, Ankit Kulshrestha, Yuan Liu, Juan Jos\'e Mendoza-Arenas, Kaushik P. Seshadreesan, Sarvagya Upadhyay, Xueyue Zhang, Quntao Zhuang, Junyu Liu
arXiv:2606. 29966v1 Announce Type: cross Abstract: Quantum computing provides a powerful paradigm for representing and transforming high-dimensional information through superposition, entanglement, and measurement-induced nonlinear features.
By Xindian Ma, Xinyu Long, Yefei Zhang, Yanchen Liu, Xianghao Li, Yufu Wen, Yike Hu, Yuedong Zhu, Zeyang Ma, Wen Qin, Yikun Wang, Peng Yang, Monan Wang, Teng Yu
arXiv:2502. 00037v4 Announce Type: replace-cross Abstract: We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states.
By Mikhail Gennadievich Belov, Victor Victorovich Dubov, Vadim Konstantinovich Ivanov, Alexander Yurievich Maslov, Olga Vladimirovna Proshina, Vladislav Gennadievich Malyshkin
arXiv:2606. 11240v1 Announce Type: cross Abstract: Accurate modeling of quantum many-body systems often requires computationally expensive simulations such as Density Matrix Renormalization Group (DMRG) or Quantum Monte Carlo (QMC) calculations.
By Arpan Biswas, Surtirtha Paul, Joseph Agada, Matthias Thamm, Adrian Del Maestro
arXiv:2605. 00330v2 Announce Type: replace Abstract: Operator learning enables fast surrogate modeling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: quadratic inference complexity and unreliable uncertainty quantification in safety-critical settings.
By Purav Matlia, Christian Moya, Guang Lin
arXiv:2607. 16281v1 Announce Type: cross Abstract: The analysis of highly non-linear stochastic data within non-equilibrium dynamical systems requires computational frameworks capable of detecting latent phase transitions before systemic structural breakdowns occur.
By Manoj B. Bhatkar, Prashant M. Yawalkar
arXiv:2606. 20326v1 Announce Type: new Abstract: We develop QCPIKAN, the first quantum-classical physics-informed Kolmogorov-Arnold network designed to solve partial differential equations (PDEs).
By Xiang Rao, Yuxuan Shen