Real-time Dynamics in 3D for up to 1000 Qubits with Neural Quantum States: Quenches and the Quantum Kibble--Zurek Mechanism

Quantum Physics [Submitted on 6 Apr 2026] Real-time Dynamics in 3D for up to 1000 Qubits with Neural Quantum States: Quenches and the Quantum Kibble--Zurek Mechanism Vighnesh Dattatraya Naik, Zheng-Hang Sun, Markus Heyl Exponential complexity of many-body wave functions limits accurate numerical simulations of real-time dynamics, especially beyond 1D, where rapid entanglement growth poses severe challenges. Neural Quantum States (NQS) have emerged as a powerful approach for real-time dynamics in 2D, but their scalability and accuracy in 3D have remained an open challenge. Here, we establish NQS as a scalable framework for 3D quantum dynamics by introducing a residual-based convolutional architecture tailored to cubic spin lattices. Focusing on the 3D transverse-field Ising model, we demonstrate that NQS reliably capture distinct quench regimes, including collapse-and-revival dynamics and, most challengingly, the dynamics following a sudden quench to the quantum critical point. We perform finite-rate quenches to the critical point on lattices containing up to 1000 qubits, an unprecedented system size for numerical simulations of real-time dynamics beyond 1D. This enables the first large-scale numerical demonstration of the 3D quantum Kibble--Zurek mechanism. The QKZM in 3D is particularly intriguing because it lies at the upper critical dimension of the Ising universality class, where the standard power laws are modified by logarithmic factors together with prominent sub-leading logarithmic corrections. By deriving these corrections from renormalization-group flow equations up to two-loop order, we obtain a robust data collapse across all simulated system sizes for the correlation function, the excess energy, and the quantum Fisher information, the latter revealing universal multipartite-entanglement dynamics. In all cases, we find compelling agreement with the expected scaling dimensions. Our findings establish NQS as a scalable and reliable tool for exploring nonequilibrium phenomena in 3D quantum matter and for providing numerical benchmarks for 3D quantum simulators. Subjects: Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other) Cite as: arXiv:2604.05032 [quant-ph]   (or arXiv:2604.05032v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.05032 Focus to learn more Submission history From: Vighnesh Dattatraya Naik [view email] [v1] Mon, 6 Apr 2026 18:00:04 UTC (7,325 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cond-mat cond-mat.other References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)