arXiv subjects

Yuntian Gu

Publications and source records attributed to Yuntian Gu.

14 recordsLinked to original sources

arXiv2026

Spin-charge separation in the triangular-lattice Hofstadter-Hubbard model

Recent experiments in moir\'e materials have enabled the realization of a variety of exotic quantum phases. In this context, the Hofstadter-Hubbard model has been proposed as a possible setting for hosting chiral spin liquid. Concurrently, significant progress has been recently made in the computational methods for two-dimensional many-body fermion systems, which makes numerically studying this challenging model a real possibility in genuine 2D geometry. Motivated by these advances, we investigate the putative chiral spin liquid phase in the triangular-lattice Hofstadter-Hubbard model using variational Monte Carlo with neural quantum states (NQS) and projected entangled pair states (PEPS). We observe spin-charge separation directly in real space through numerical spin-pumping simulation and real-time spin and charge motion. In addition, in the context of anyonic superconductivity conjectured in this model, we find a positive two-electron binding energy on small systems, but it decreases below our numerical resolution as the system size increases. Our work demonstrates NQS and PEPS as powerful tools, capable of cross-checking each other, for diagnosing topological order and fractionalized excitations in strongly correlated electronic systems.

cond-mat.str-el↗

arXiv2026

Exact Neural-Network Representations of the Motzkin States

Motzkin spin chains are paradigmatic frustration-free one-dimensional quantum systems whose ground states feature exactly solvable combinatorial structures and exotic, area-law-violating entanglement scaling. Specifically, colorless Motzkin states exhibit critical logarithmic entanglement divergence $\log N$ with system size $N$, while their colorful counterparts host supercritical sublinear $\sqrt{N}$ entanglement growth. Such unconventional entanglement behaviors place these states well beyond the expressive capability of standard matrix product states, which are fundamentally constrained by the entanglement area law. Here, we systematically construct exact, training-free neural-network representations for both colorless and colorful Motzkin states across four mainstream architectures, including recurrent, feedforward, convolutional, and transformer networks. Our core design leverages a causal prefix-sum module, implementable via recurrent updates, feedforward mappings, or masked attention layers, combined with position-selective rectified linear gates that enforce the Motzkin height constraints. For the colorful states, we further introduce a dedicated causal stack module that explicitly encodes the last-in-first-out color-matching rule. Our results demonstrate that neural architectures can accurately capture highly non-trivial entanglement features inaccessible to conventional tensor networks, providing prototypic examples for benchmarking and a constructive design framework for future neural-network quantum state developments targeting strongly entangled quantum systems.

cond-mat.str-el↗

arXiv2026

Quantum-classical crossover in fault-tolerant quantum dynamics simulation

While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics under realistic hardware conditions. We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations, suppressing the residual logical errors that limit existing partially fault-tolerant approaches. A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics at modest system sizes. For a physical error rate of $p=10^{-3}$, fault-tolerant simulation requires approximately 2 hours and $3.7 \times 10^5$ physical qubits for a 100-site 1D system, whereas tensor network approaches would require about 100 years. For 2D models, where rapid entanglement growth limits the classical evolution time, we project quantum runtimes within minutes. A physical error rate of $p=10^{-4}$ leads to at least an order of magnitude reduction in qubit count ($3.1 \times 10^4$ physical qubits) and runtime (minutes for 1D and seconds for 2D). The reduction in quantum runtime arises from our improved rotation-state injection and co-design of quantum error correction and observable-estimation protocols, which jointly suppress logical-error accumulation and reduce sampling overhead. Our results establish a scalable route towards practical quantum advantage and identify quantitative engineering targets for future fault-tolerant architectures.

quant-ph↗

arXiv2026

Pareto Frontier of Neural Quantum States: Scalable, Affordable, and Accurate Convolutional Backflow for Strongly Correlated Lattice Fermions

Neural Quantum States (NQS) are now among the most accurate methods for studying strongly correlated many-fermion systems, outperforming existing many-body approaches for large systems. However, NQS calculations remain extremely resource-intensive. Here, we introduce a new Pareto frontier of efficiency and accuracy for NQS in simulating strongly correlated lattice fermions, defined by two complementary backflow-related architectures: the Sparse Convolutional Ansatz for Lattice Electrons (SCALE) (state-of-the-art efficiency) and the Accurate Convolutional ansatz for lattice Electrons (ACE) (state-of-the-art accuracy), benchmarked on the iconic Hubbard and $t-J$ models for large lattices. SCALE uses a tailored convolutional design enabling efficient local updates via low-rank determinant updates, reducing computational scaling from $O(N^4)$ to $O(N^3)$ in backflow methods and yielding a >40$\times$ practical speed-up in tests while maintaining high variational accuracy. As an application, we study the previously inaccessible 1/8-doped pure Hubbard model up to $32 \times 32$, finding no significant energy difference between horizontal and vertical filled stripe states - contrasting with half-filled stripe states when next-nearest-neighbor hoppings are included. ACE employs a deep convolutional stack to maximize expressive power, achieving unprecedented accuracy on large systems. Extensive benchmarks on Hubbard and $t-J$ models show SCALE delivers variational energies competitive with leading methods at a fraction of the cost, while ACE sets a new accuracy benchmark, surpassing recent results with only 1/6 the runtime for $16 \times 4$ systems. These new NQS approaches provide scalable, affordable, and accurate tools for exploring strongly correlated fermionic physics, such as the microscopic mechanism of unconventional superconductivity.

cond-mat.str-el↗

arXiv2026

Disentangling Tensor Network States with Deep Neural Network

We introduce Neural Tensor Network States ($\nu$TNS), a variational many-body wave-function ansatz that integrates deep neural networks with tensor-network architectures. In the $\nu$TNS framework, a neural network serves as a disentangler of the wave-function, transforming the physical degrees of freedom into renormalized variables with much less entanglement. The renormalized state is then efficiently encoded by a back-flow tensor network. This construction yields a compact yet highly expressive representation of strongly correlated quantum states. Using convolutional neural networks combined with matrix product states as a concrete implementation, we obtain state-of-the-art variational energies for the spin-$1/2$ $J_1$-$J_2$ Heisenberg model on the square lattice at the highly frustrated point $J_2/J_1=0.5$, for systems up to $20\times 20$ with periodic boundary conditions. Finite-size scaling of spin, dimer, and plaquette correlations exhibits power-law decay without magnetic or valence-bond long-range order, consistent with a gapless quantum spin-liquid ground state at that point.This $\nu$TNS framework is flexible and naturally extensible to other neural and tensor-network structures, offering a general platform for investigating strongly correlated quantum many-body systems.

cond-mat.str-el↗

arXiv2025

Solving the Hubbard model with Neural Quantum States

The rapid development of neural quantum states (NQS) has established it as a promising framework for studying quantum many-body systems. In this work, by leveraging the cutting-edge transformer-based architectures and developing highly efficient optimization algorithms, we achieve the state-of-the-art results for the doped two-dimensional (2D) Hubbard model, arguably the minimum model for high-Tc superconductivity. Interestingly, we find different attention heads in the NQS ansatz can directly encode correlations at different scales, making it capable of capturing long-range correlations and entanglements in strongly correlated systems. With these advances, we establish the half-filled stripe in the ground state of 2D Hubbard model with the next nearest neighboring hoppings, consistent with experimental observations in cuprates. Our work establishes NQS as a powerful tool for solving challenging many-fermions systems.

cond-mat.str-el↗

arXiv2024

How Numerical Precision Affects Arithmetical Reasoning Capabilities of LLMs

Despite the remarkable success of Transformer-based large language models (LLMs) across various domains, understanding and enhancing their mathematical capabilities remains a significant challenge. In this paper, we conduct a rigorous theoretical analysis of LLMs' mathematical abilities, with a specific focus on their arithmetic performances. We identify numerical precision as a key factor that influences their effectiveness in arithmetical tasks. Our results show that Transformers operating with low numerical precision fail to address arithmetic tasks, such as iterated addition and integer multiplication, unless the model size grows super-polynomially with respect to the input length. In contrast, Transformers with standard numerical precision can efficiently handle these tasks with significantly smaller model sizes. We further support our theoretical findings through empirical experiments that explore the impact of varying numerical precision on arithmetic tasks, providing valuable insights for improving the mathematical reasoning capabilities of LLMs.

cs.LG↗

arXiv2024

Towards Differentiable Multilevel Optimization: A Gradient-Based Approach

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently handling the nested structure. This paper introduces a novel gradient-based approach for multilevel optimization that overcomes these limitations by leveraging a hierarchically structured decomposition of the full gradient and employing advanced propagation techniques. Extending to n-level scenarios, our method significantly reduces computational complexity while improving both solution accuracy and convergence speed. We demonstrate the effectiveness of our approach through numerical experiments, comparing it with existing methods across several benchmarks. The results show a notable improvement in solution accuracy. To the best of our knowledge, this is one of the first algorithms to provide a general version of implicit differentiation with both theoretical guarantees and superior empirical performance.

cs.LG↗

arXiv2024

QCircuitBench: A Large-Scale Dataset for Benchmarking Quantum Algorithm Design

Quantum computing is an emerging field recognized for the significant speedup it offers over classical computing through quantum algorithms. However, designing and implementing quantum algorithms pose challenges due to the complex nature of quantum mechanics and the necessity for precise control over quantum states. Despite the significant advancements in AI, there has been a lack of datasets specifically tailored for this purpose. In this work, we introduce QCircuitBench, the first benchmark dataset designed to evaluate AI's capability in designing and implementing quantum algorithms using quantum programming languages. Unlike using AI for writing traditional codes, this task is fundamentally more complicated due to highly flexible design space. Our key contributions include: 1. A general framework which formulates the key features of quantum algorithm design for Large Language Models. 2. Implementations for quantum algorithms from basic primitives to advanced applications, spanning 3 task suites, 25 algorithms, and 120,290 data points. 3. Automatic validation and verification functions, allowing for iterative evaluation and interactive reasoning without human inspection. 4. Promising potential as a training dataset through preliminary fine-tuning results. We observed several interesting experimental phenomena: LLMs tend to exhibit consistent error patterns, and fine-tuning does not always outperform few-shot learning. In all, QCircuitBench is a comprehensive benchmark for LLM-driven quantum algorithm design, and it reveals limitations of LLMs in this domain.

quant-ph↗

arXiv2024

$\widetilde{O}(N^2)$ Representation of General Continuous Anti-symmetric Function

In quantum mechanics, the wave function of fermion systems such as many-body electron systems are anti-symmetric (AS) and continuous, and it is crucial yet challenging to find an ansatz to represent them. This paper addresses this challenge by presenting an ${\widetilde O}(N^2)$ ansatz based on permutation-equivariant functions. We prove that our ansatz can represent any AS continuous functions, and can accommodate the determinant-based structure proposed by Hutter [14], solving the proposed open problems that ${O}(N)$ Slater determinants are sufficient to provide universal representation of AS continuous functions. Together, we offer a generalizable and efficient approach to representing AS continuous functions, shedding light on designing neural networks to learn wave functions.

quant-ph↗

arXiv2023

Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective

Recent studies have discovered that Chain-of-Thought prompting (CoT) can dramatically improve the performance of Large Language Models (LLMs), particularly when dealing with complex tasks involving mathematics or reasoning. Despite the enormous empirical success, the underlying mechanisms behind CoT and how it unlocks the potential of LLMs remain elusive. In this paper, we take a first step towards theoretically answering these questions. Specifically, we examine the expressivity of LLMs with CoT in solving fundamental mathematical and decision-making problems. By using circuit complexity theory, we first give impossibility results showing that bounded-depth Transformers are unable to directly produce correct answers for basic arithmetic/equation tasks unless the model size grows super-polynomially with respect to the input length. In contrast, we then prove by construction that autoregressive Transformers of constant size suffice to solve both tasks by generating CoT derivations using a commonly used math language format. Moreover, we show LLMs with CoT can handle a general class of decision-making problems known as Dynamic Programming, thus justifying its power in tackling complex real-world tasks. Finally, an extensive set of experiments show that, while Transformers always fail to directly predict the answers, they can consistently learn to generate correct solutions step-by-step given sufficient CoT demonstrations.

cs.LG↗

arXiv2023

FLatS: Principled Out-of-Distribution Detection with Feature-Based Likelihood Ratio Score

Detecting out-of-distribution (OOD) instances is crucial for NLP models in practical applications. Although numerous OOD detection methods exist, most of them are empirical. Backed by theoretical analysis, this paper advocates for the measurement of the "OOD-ness" of a test case $\boldsymbol{x}$ through the likelihood ratio between out-distribution $\mathcal P_{\textit{out}}$ and in-distribution $\mathcal P_{\textit{in}}$. We argue that the state-of-the-art (SOTA) feature-based OOD detection methods, such as Maha and KNN, are suboptimal since they only estimate in-distribution density $p_{\textit{in}}(\boldsymbol{x})$. To address this issue, we propose FLatS, a principled solution for OOD detection based on likelihood ratio. Moreover, we demonstrate that FLatS can serve as a general framework capable of enhancing other OOD detection methods by incorporating out-distribution density $p_{\textit{out}}(\boldsymbol{x})$ estimation. Experiments show that FLatS establishes a new SOTA on popular benchmarks. Our code is publicly available at https://github.com/linhaowei1/FLatS.

cs.LG↗

arXiv2023

Denoising Masked AutoEncoders Help Robust Classification

In this paper, we propose a new self-supervised method, which is called Denoising Masked AutoEncoders (DMAE), for learning certified robust classifiers of images. In DMAE, we corrupt each image by adding Gaussian noises to each pixel value and randomly masking several patches. A Transformer-based encoder-decoder model is then trained to reconstruct the original image from the corrupted one. In this learning paradigm, the encoder will learn to capture relevant semantics for the downstream tasks, which is also robust to Gaussian additive noises. We show that the pre-trained encoder can naturally be used as the base classifier in Gaussian smoothed models, where we can analytically compute the certified radius for any data point. Although the proposed method is simple, it yields significant performance improvement in downstream classification tasks. We show that the DMAE ViT-Base model, which just uses 1/10 parameters of the model developed in recent work arXiv:2206.10550, achieves competitive or better certified accuracy in various settings. The DMAE ViT-Large model significantly surpasses all previous results, establishing a new state-of-the-art on ImageNet dataset. We further demonstrate that the pre-trained model has good transferability to the CIFAR-10 dataset, suggesting its wide adaptability. Models and code are available at https://github.com/quanlin-wu/dmae.

cs.CV↗

arXiv2022

Guided Diffusion Model for Adversarial Purification from Random Noise

In this paper, we propose a novel guided diffusion purification approach to provide a strong defense against adversarial attacks. Our model achieves 89.62% robust accuracy under PGD-L_inf attack (eps = 8/255) on the CIFAR-10 dataset. We first explore the essential correlations between unguided diffusion models and randomized smoothing, enabling us to apply the models to certified robustness. The empirical results show that our models outperform randomized smoothing by 5% when the certified L2 radius r is larger than 0.5.

cs.LG↗