arXiv subjects

Xianquan Yan

Publications and source records attributed to Xianquan Yan.

4 recordsLinked to original sources

arXiv2026

Topological classification through knotted graphs: Fermi surface dispersions and Lifshitz transitions

Knot theory has provided a rich topological taxonomy for band structures, but its reach is fundamentally limited: knot invariants classify only 1D nodal lines at gap closure, and cannot encode the full dispersion or rich Fermi surface structure of realistic materials. Here we show that knotted graphs (knots that admit graph-like intersections in 3D space) - which have so far been elusive in condensed matter literature - provide a unified topological language for classifying the entire band dispersion, and even the eigenstate topology in some contexts. We propose a new framework beyond the existing Yamada polynomials that can topologically characterize the intricacies of realistic Fermi surfaces completely, crucially including how their multiple disconnected pieces are nested. This yields the Yamada set, a boundary-resolved extension which organizes the full topological evolution across energy into a Yamada sequence: a compact dispersion-level fingerprint directly tied to experimental signatures of Lifshitz transitions. Our framework is demonstrated with DFT-based band structures of real materials. Beyond dispersion-level classifications, this framework can be extended to non-Hermitian exceptional surfaces, where Berry-curvature flux further equips the knotted-graph skeleton with a directed Abelian edge flow that also captures the eigenstate topology.

cond-mat.mes-hall↗

arXiv2026

Practical Error Suppression and Mitigation for Reliable Quantum Computing

Quantum computing is entering a transitional regime between noisy intermediate-scale quantum (NISQ) processing and early fault-tolerant quantum computation (FTQC), in which increasingly capable hardware is beginning to support repeated syndrome measurements, partial error correction, and logical-qubit operations, while residual physical and logical errors remain non-negligible. In this regime, error suppression, error mitigation, and quantum error correction are increasingly better viewed as complementary layers of a unified error-reduction strategy rather than as separate approaches, with each acting at a different stage of the quantum computation to improve simulation reliability. Thus, in this review, we provide a practical and forward-looking overview of the principal hardware error sources and the corresponding error suppression and mitigation methods for reducing their impact across the current NISQ-FTQC transition. We discuss hardware-aware circuit design, coherent-error suppression, readout mitigation, noise extrapolation, classical inference, and software-supported workflows, with particular emphasis on their implementation on actual quantum processors. We further examine how error mitigation techniques can be adapted to encoded and logical-qubit settings so that they can operate alongside quantum error correction to suppress residual logical errors and improve the accuracy of computation in the early fault-tolerant regime.

quant-ph↗

arXiv2026

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

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 Poly2Graph: a high-performance, open-source pipeline that automates the mapping of 1-D crystal Hamiltonians to spectral graphs. Using this tool, we present 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.

cs.LG↗

arXiv2026

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

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.

cond-mat.stat-mech↗