arXiv subjects

Lixing Zhang

Publications and source records attributed to Lixing Zhang.

12 recordsLinked to original sources

arXiv2026

Foundation Neural Effective Hamiltonian for Strongly Correlated Quantum Materials

Simulating strongly correlated quantum materials often involves not a single Hamiltonian, but a family of Hamiltonians whose ground states evolve across experimentally tunable couplings. Foundation neural quantum states (FNQS) offer a promising route to amortizing many-body calculations across such families, but can lose accuracy near phase transitions and still incur non-negligible sampling costs that grow with the number of target couplings. We introduce the Foundation Neural Effective Hamiltonian (FNEH), which projects a Hamiltonian family onto a compact subspace spanned by FNQS sampled at selected couplings. By variationally combining FNQS across parameter space, FNEH systematically improves their ground-state approximation and can recover phase boundaries that the foundation model misidentifies. Once the required operator matrix elements are sampled, FNEH enables sweeps over couplings, observables, and phase boundaries at a cost governed by the small effective-Hamiltonian dimension, without repeated neural-network sampling at every target coupling. We demonstrate FNEH in strongly correlated moir\'e materials, where it accurately resolves competing phases, enables high-resolution multidimensional phase scans, and substantially reduces the computational cost of exploring many target Hamiltonians. The results open a new avenue for studying strongly correlated quantum materials with foundation models.

quant-ph↗

arXiv2026

Learning What Not to Impute: An Uncertainty-Aware Diffusion Framework for Meaningful Missingness

Missing value imputation is a fundamental task in machine learning, with most existing methods assuming that all missing entries correspond to unobserved regular values. In many real-world datasets, however, missingness may arise from two distinct sources: some entries are meaningfully missing (intrinsically absent and semantically valid), while others are missing due to the observation process and should be imputed. We formalize this distinction as a selective imputation problem, where the goal is to jointly infer which missing entries should be preserved and which should be recovered. To address this challenge, we propose Diff-Joint, a diffusion-based framework that jointly models tabular data together with a latent missingness mask. The method alternates between conditional sampling and uncertainty-aware aggregation to iteratively refine both imputed values and missingness labels. Empirical results on synthetic and real-world datasets demonstrate that Diff-Joint effectively identifies meaningfully missing entries while achieving competitive imputation accuracy and improved downstream task performance.

cs.LG↗

arXiv2026

WF-Bench: A Benchmark for Neural Network WaveFunction Expressivity and Scaling Laws

We present a comprehensive benchmarking dataset and empirical scaling law analysis for neural network wavefunctions by matching them to a wide spectrum of famous many body target wavefunctions. The dataset, WF-Bench, spans multiple distinct regimes of strongly correlated quantum matter, including topological states, Wigner crystals, and superconducting wavefunctions, providing a diverse and challenging test bed for neural network wavefunction expressivity. We introduce a systematic and reproducible benchmarking protocol for target wavefunction matching, enabling consistent performance evaluation across different neural network wavefunction architectures. By using wavefunction fidelity as the uniform metric, we discover empirical scaling laws that characterize how representability depends on system size and key model parameters, including number of determinant and model depth. By applying our benchmark protocol on Psiformer and Ferminet, we show that WF-Bench establishes a unified dataset driven framework for evaluating and comparing neural network wavefunctions and for guiding the design of future architectures.

physics.comp-ph↗

arXiv2026

Masked Diffusion Modeling for Anomaly Detection

Anomaly detection aims to identify samples that deviate from the nominal data distribution and is central to many safety-critical applications. However, developing effective anomaly detection methods for categorical, mixed-type, and discrete sequence data remains challenging and relatively underexplored. Masked diffusion models provide a natural way to model such data by learning to recover masked values from the remaining visible context. In this paper, we propose Masked Diffusion for Anomaly Detection (MaskDiff-AD), a forward-only method based on masked diffusion models trained only on nominal data. Given a test sample, MaskDiff-AD constructs anomaly scores from the difficulty of reconstructing randomly masked coordinates, yielding a content-sensitive score that operates directly on discrete state spaces while avoiding reverse-time sampling. We also develop a non-parametric variant of MaskDiff-AD and provide theoretical guarantees by characterizing Type-I and Type-II errors under a fixed detection threshold. Experiments on fourteen categorical and mixed-type tabular datasets from ADBench and UADAD, as well as four text anomaly detection datasets from NLP-ADBench, show that MaskDiff-AD achieves competitive performance against classical, diffusion-based, and recent tabular/text anomaly detection baselines. Notably, MaskDiff-AD achieves the best overall average rank, outperforming all twelve tabular baseline methods.

cs.LG↗

arXiv2026

ParamSpMM: Adaptive and Efficient Sparse Matrix-Matrix Multiplication on GPUs for GNNs

Fueled by the ability to mine real-world graph data, GNN applications have experienced phenomenal growth. Sparse Matrix-Matrix Multiplication (SpMM) is a critical operator in GNNs. However, existing SpMM designs for GNNs struggle to adapt to diverse input characteristics. In this paper, we first conduct a comprehensive analysis of existing SpMM optimizations, revealing their limitations through statistical and empirical evidence. Based on this analysis, we introduce ParamSpMM, a parametric approach for highly adaptive and efficient SpMM computation in GNNs. It incorporates a new data structure, the Parameterized Compressed Sparse Row (PCSR), to flexibly integrate existing optimization techniques. ParamSpMM enables the configuration of these optimization techniques according to various input characteristics. Furthermore, we complement ParamSpMM with an ML-based SpMM-decider that predicts optimal configurations based on carefully crafted input features. Our evaluations demonstrate that ParamSpMM outperforms Nvidia cuSPARSE with an average speedup of 1.92x, significantly enhancing GNN training efficiency.

cs.DC↗

arXiv2026

The Grimmer--Shu--Wang Certificate and the Drori--Teboulle Minimax Constant-Stepsize Bound for $N\ge 3$

We prove, for every horizon $N\ge 3$, the existence of the strengthened low-rank performance-estimation certificate proposed by Grimmer, Shu, and Wang for the Drori--Teboulle constant-step gradient-descent bound. For each $N\ge 3$, let $\rho_N\in(0,1)$ be determined by $\rho_N^{2N}(2N\rho_N+2N+1)=1$. We show that the GSW certificate equations admit positive vectors $a,b,c,d$ satisfying all residual equations. The proof proceeds through a reduced residual system in the variables $d$, a simplex existence argument for a positive reduced zero, a terminal residual completion identity, and a tail-square convolution argument proving the cumulative margins that force $b>0$ and then $a>0$. Consequently, the GSW low-rank PEP certificate exists for every $N\ge 3$ and yields the Drori--Teboulle upper bound. We also include the one-dimensional quadratic and Huber lower-bound examples for nonnegative steps, while the quadratic example excludes negative constant steps from being optimal. Together these prove the Drori--Teboulle minimax constant-stepsize value over all real constant steps for every $N\ge 3$.

math.OC↗

arXiv2026

Sequential Change Detection for Multiple Data Streams with Differential Privacy

Sequential change-point detection seeks to rapidly identify distributional changes in streaming data while controlling false alarms. Existing multi-stream detection methods typically rely on non-private access to raw observations or intermediate statistics, limiting their usage in privacy-sensitive settings. We study sequential change-point detection for multiple data streams under differential privacy constraints. We consider multiple independent streams undergoing a synchronized change at an unknown time and in an unknown subset of streams, and propose DP-SUM-CUSUM, a differentially private detection procedure based on the summation of per-stream CUSUM statistics with calibrated Laplace noise injection. We show that DP-SUM-CUSUM satisfies sequential $\varepsilon$-differential privacy and derive bounds on the average run length to false alarm and the worst-case average detection delay, explicitly characterizing the privacy--efficiency tradeoff. A truncation-based extension is also presented to handle distributional shifts with unbounded log-likelihood ratios. Simulations and experiments on an Internet of Things (IoT) botnet dataset validate the proposed approach.

math.ST↗

arXiv2025

Continuous Variable Hamiltonian Learning at Heisenberg Limit via Displacement-Random Unitary Transformation

Characterizing continuous-variable (CV) Hamiltonians can be formulated as Hamiltonian learning under quantum measurement constraints: finite operator coefficients are inferred from noisy measurement outcomes obtained by probing an infinite-dimensional system. Existing Heisenberg-limited CV protocols are often limited to low-order structures, vulnerable to noise, or unresolved for generic multi-mode settings. We introduce Displacement-Random Unitary Transformation (D-RUT), an active data acquisition protocol with pre-specified probes and number-preserving transformations that reduce finite-order bosonic Hamiltonian learning to polynomial recovery. We prove Heisenberg-limited total evolution time with robustness to state preparation and measurement (SPAM) errors, and develop hierarchical multi-mode coefficient recovery with better statistical efficiency than simultaneous estimation. We also extend D-RUT to first-quantized Hamiltonian coefficient learning, and numerical experiments on single- and multi-mode nonlinear systems validate the predicted Heisenberg scaling.

quant-ph↗

arXiv2025

Neural Transformer Backflow for Solving Momentum-Resolved Ground States of Strongly Correlated Materials

Strongly correlated materials host a rich variety of exotic quantum phases but remain challenging to solve due to strong interactions. We introduce the Neural Transformer Backflow (NTB) framework, a powerful neural-network ansatz formulated within a multi-band projection formalism. NTB is mean-field transcendental, parameter-efficient and fermionic intrinsic, exhibiting superior performance compared with existing neural ansatzes. By naturally enforcing momentum conservation, NTB enables direct computation of momentum-resolved many-body ground states, providing detailed access to degeneracies and energy gaps. It achieves high accuracy on small systems and scales efficiently to larger sizes and higher-band truncations far beyond the reach of exact diagonalization. We demonstrate the power of NTB in capturing diverse correlated phases in twisted MoTe$_2$, including charge density waves, fractional Chern insulators, and anomalous Hall Fermi liquids, within a unified framework. This approach offers a generic, scalable route towards understanding and discovering quantum phases in strongly correlated materials.

cond-mat.str-el↗

arXiv2025

Hamiltonian Learning at Heisenberg Limit for Hybrid Quantum Systems

Hybrid quantum systems with different particle species are fundamental in quantum materials and quantum information science. In this work, we establish a rigorous theoretical framework proving that, given access to an unknown spin-boson type Hamiltonian, our algorithm achieves Heisenberg-limited estimation for all coupling parameters up to error $\epsilon$ with a total evolution time ${O}(\epsilon^{-1})$ using only ${O}({\rm polylog}(\epsilon^{-1}))$ measurements. It is also robust against small state preparation and measurement errors. In addition, we provide an alternative algorithm based on distributed quantum sensing, which significantly reduces the evolution time per measurement. To validate our method, we demonstrate its efficiency in hybrid Hamiltonian learning and spectrum learning, with broad applications in AMO, condensed matter and high energy physics. Our results provide a scalable and robust framework for precision Hamiltonian characterization in hybrid quantum platforms.

quant-ph↗

arXiv2023

Dissipative Landau-Zener transitions in a three-level bow-tie model: accurate dynamics with the Davydov multi-D2 Ansatz

We investigate Landau-Zener (LZ) transitions in the three-level bow-tie model (3L-BTM) in a dissipative environment by using the numerically accurate method of multiple Davydov D2 Ansatze. We first consider the 3L-TBM coupled to a single harmonic mode, study evolutions of the transition probabilities for selected values of the model parameters, and interpret the obtained results with the aid of the energy diagram method. We then explore the 3L-TBM coupled to a boson bath. Our simulations demonstrate that sub-Ohmic, Ohmic and super-Ohmic boson baths have substantially different influences on the 3L-BTM dynamics, which cannot be grasped by the standard phenomenological Markovian single-rate descriptions. We also describe novel bath-induced phenomena which are absent in two-level LZ systems.

quant-ph↗

arXiv2023

Dynamics of dissipative Landau-Zener transitions in an anisotropic three-level system

We investigate the dynamics of Landau-Zener transitions in an anisotropic, dissipative three-level model (3-LZM) using the numerically accurate multiple Davydov D2 Ansatz in the framework of time-dependent variation. It is demonstrated that a non-monotonic relationship exists between the Landau-Zener transition probability and the phonon coupling strength when the 3-LZM is driven by a linear external field. Under the influence of a periodic driving field, phonon coupling may induce peaks in contour plots of the transition probability when the magnitude of the system anisotropy matches the phonon frequency. Dynamics of the 3-LZM have also been probed in the presence of a super-ohmic phonon bath when driven by a periodic driving field. It is found that both the period and the amplitude of the Rabi cycle decay exponentially with the increasing bath coupling strength.

quant-ph↗