Xianquan Yan

Xianquan Yan

Ph.D. Candidate @ NUS
{Physics, CS} Dept
Condensed Matter Physics, AI for Physics, Quantum Information Science, and Complex Systems.

Posts by Collection

publications

Deterministic scale-invariant dynamics in a logistic Game-of-Life model

Communications Physics [Nature Portfolio] (to appear), 2025-June

Abstract: Scale invariance is a hallmark of criticality in complex dynamical systems. While random external inputs or tunable stochastic interactions are typically required to produce critical behavior, it remains unclear whether scale-invariant dynamics can emerge from purely deterministic interactions. Here, we address this question by studying the asymptotic dynamics of the logistic Game of Life (GOL), a deterministic-parameter extension of Conway’s GOL. In this system, we identify three distinct asymptotic phases separated by two fundamentally different critical points. The first critical point, associated with an unusual form of self-organized criticality, separates a sparse-static phase from a sparse-dynamic phase. The second critical point corresponds to a deterministic percolation transition between the sparse-dynamic phase and a third, dense-dynamic phase. In addition, we observe power-law cluster size distributions with unconventional critical exponents not found in standard equilibrium systems. Overall, our work paves the way for studying emergent scale invariance in purely deterministic systems.

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Precise Identification of Topological Phase Transitions with Eigensystem-Based Clustering

AI4X 2025 International Conference, 2025-July

Abstract: Recent advances in machine learning have spurred new ways to explore and classify quantum phases of matter. We propose an Eigensystem-based representation, combined with a Gaussian Mixture Model (GMM), to unsupervisedly cluster Hamiltonians into distinct topological phases with minimal feature engineering. The method identifies different topological phases without any prior knowledge, pinpoints phase boundaries with remarkable precision \(\sim\mathcal{O}(10^{-5})\), remains robust under moderate noise, and scales efficiently via a simple dimensionality-reduction step. The success of GMM offers a novel physical insight — each phase forms a well-separated multivariate Gaussian in a high-dimensional “Eigensystem space.” We illustrate the approach on several 1D lattice models, all achieving near 100% accuracies.

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Automated Metric Discovery: Navigating Quantum Geometry with Symbolic Regression

AI4X 2025 International Conference, 2025-July

Abstract: I demonstrated how symbolic regression can \(\textit{automatically learn}\) quantum geometric metrics from numerical data, recovering known formulas (e.g. Fubini-Study and Bures) in a transparent, closed-form fashion. Beyond these canonical examples, the same approach opens the door to exploring \(\textit{customized}\) quantum metrics that maximize a problem-specific objective.

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Classifying the Graph Topology of Non-Hermitian Energy Spectra with Graph Transformer.

AAAI 2026 XAI4Science Workshop, 2025-November

Abstract: Classifying non-Hermitian energy spectra under open boundary conditions is an open challenge in physics. This classification is a critical prerequisite for the rational inverse design of systems exhibiting desired dynamics and topological responses. While graph topology has emerged as a promising approach for characterizing these spectra, systematic methods for distilling non-Hermitian spectra into their corresponding graph representations have been lacking. Moreover, the resulting graphs often exhibit complexities that defy manual classification, necessitating machine learning approaches. In this work, we introduce a two-step framework for classifying non-Hermitian spectra based on their graph topologies. The first step employs Poly2Graph, an automated, high-performance pipeline that distills non-Hermitian spectra into spectral graphs suitable for graph neural networks (GNNs). The second step involves generating a large dataset of these spectral graphs and training a GNN for classification. We propose GnLTransformer, a novel architecture featuring dual channels that leverage line graphs to explicitly capture higher-order topological features. GnLTransformer achieves over 99% classification accuracy on our dataset, outperforming standard baselines by 32%. Notably, beyond conventional GNNs, GnLTransformer offers inherent explainability regarding higher-order topology. As a further contribution, we release a new multi-graph dataset comprising over 117K spectral graphs.

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HSG-12M: A Large-Scale Benchmark of Spatial Multigraphs from the Energy Spectra of Non-Hermitian Crystals

The Fourteenth International Conference on Learning Representations (ICLR 2026), 2026-January

Abstract: AI is transforming scientific research by revealing new ways to understand complex physical systems, but its impact remains constrained by the lack of large, high-quality domain-specific datasets. A rich, largely untapped resource lies in non-Hermitian quantum physics, where the energy spectra of crystals form intricate geometries on the complex plane—termed as Hamiltonian spectral graphs. Despite their significance as fingerprints for electronic behavior, their systematic study has been intractable due to the reliance on manual extraction. To unlock this potential, we introduce \(\href{https://github.com/sarinstein-yan/Poly2Graph}{\texttt{Poly2Graph}}\): a high-performance, open-source pipeline that automates the mapping of 1-D crystal Hamiltonians to spectral graphs. Using this tool, we present \(\href{https://github.com/sarinstein-yan/HSG-12M}{\texttt{HSG-12M}}\): a dataset containing 11.6 million static and 5.1 million dynamic Hamiltonian spectral graphs across 1401 characteristic-polynomial classes, distilled from 177 TB of spectral potential data. Crucially, HSG-12M is the first large-scale dataset of spatial multigraphs—graphs embedded in a metric space where multiple geometrically distinct trajectories between two nodes are retained as separate edges. This simultaneously addresses a critical gap, as existing graph benchmarks overwhelmingly assume simple, non-spatial edges, discarding vital geometric information. Benchmarks with popular GNNs expose new challenges in learning spatial multi-edges at scale. Beyond its practical utility, we show that spectral graphs serve as universal topological fingerprints of polynomials, vectors, and matrices, forging a new algebra-to-graph link. HSG-12M lays the groundwork for data-driven scientific discovery in condensed matter physics, new opportunities in geometry-aware graph learning and beyond.

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