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Shuai Zeng

Publications and source records attributed to Shuai Zeng.

16 recordsLinked to original sources
arXiv2026

An exact hierarchy for Lebesgue's universal covering constant and a certified 0.834 lower bound

Posed by Lebesgue in 1914, the universal covering problem asks for the smallest-area planar convex set containing a congruent copy of every set of diameter at most one. We introduce an exact Reuleaux-type variational hierarchy for this constant: its monotone finite-arc values $\Lambda_M$ satisfy $a_{\mathrm{Leb}}=\lim_{M\to\infty}\Lambda_M$, and each level is a continuous finite-dimensional problem. We prove $0\le a_{\mathrm{Leb}}-\Lambda_M\le C M^{-2}$, giving a controlled finite-arc route to the constant itself. As a certified low-order realization, an outward-rounded interval certificate for a regular finite Reuleaux subtest proves $a_{\mathrm{Leb}}\ge0.834$, improving the lower-bound benchmark established by Brass and Sharifi in 2005.

math.MG↗
arXiv2026

Postselection-Free Reconstruction of Monitored SPT Flux-Charge Responses

A class of monitored topological invariants compares ordinary and symmetry-twisted quantum trajectories with identical stochastic records, so direct estimation requires exponentially costly matched-record postselection. We replace the twisted quantum experiment by uniformly randomized symmetry eigenstates with known charges, ordinary-boundary monitoring, and an offline twist decoder. Their correlation yields an exact finite-time response identity and removes this experimental sampling bottleneck. When the ordinary charge sharpens and the ordinary-to-flux deformation has trivial net readout-character flow, the response converges to the projective commutator of the symmetry-protected-topological phase; generator-pair responses then determine its finite-Abelian cohomology class. Spectator-sector crossings may close the global Lyapunov gap without changing this character-valued response. In monitored cluster circuits, the decoder is exact and polynomial in the Gaussian limit, while Gaussian-drop reconstruction treats interacting records; independent joint-sector spectroscopy and effect-state diagnostics validate the topological deformation.

quant-ph↗
arXiv2026

Renormalization-group locking of finite anisotropic propagation cones in Yukawa networks

Different field species can begin with finite anisotropic propagation geometries whose principal axes need not coincide. We ask whether local Yukawa interactions on a finite graph can nevertheless generate one common infrared spatial cone, even when the interactions that drive the locking become marginally irrelevant. Retaining the full finite mismatch between positive-definite spatial kinetic matrices, we derive the one-loop nonlinear matrix flow and show that its Thompson diameter is globally nonexpansive. On a connected graph, persistent normalized edge activity upgrades this to a uniform finite-window contraction, so all interacting sectors asymptotically share one relative propagation geometry. An explicit two-channel Pauli-Dirac Yukawa-quartic completion realizes the persistence conditions on an open weak-coupling set of finite-mismatch initial data. In four dimensions the Yukawa couplings vanish in the infrared, yet their accumulated interaction time diverges, leaving a Gaussian endpoint with a common spatial cone. For a controlled two-plateau extremal class, graph distance also fixes the first nonzero short-time order of the diameter decrease. Thus common-cone locking can emerge from renormalization-group dynamics rather than being imposed as a microscopic common structure.

hep-th↗
arXiv2026

Reliability Is Not Free in Universal Quantum Work Extraction

Universal work extraction shows that input-state knowledge is unnecessary to attain the asymptotic free-energy rate. We ask whether this first-order universality extends to reliability, the exponential decay rate of extraction failure. In the work-battery fidelity formulation, we prove that no phase-independent Gibbs-preserving protocol can retain the state-aware Gibbs-preserving exponent throughout a coherent qubit time-translation orbit: at every positive target rate, its worst pointwise exponent is bounded by the corresponding state-aware thermal-operation value. The proof first establishes an exact finite-blocklength identity between phase-robust Gibbs-preserving extraction and state-aware thermal extraction. A trigonometric Remez inequality then upgrades this minimax identity to a pointwise theorem by ruling out exponential localization of the worst phase. For an explicit coherent-qubit family, known-phase Gibbs-preserving extraction is error free, whereas every phase-independent protocol has a finite worst-pointwise exponent. Thus input-state knowledge can be irrelevant to the first-order work rate yet indispensable for optimal exponential reliability.

quant-ph↗
arXiv2026

Thermal Activation of Divergent Distillable Entanglement under Non-Abelian Strong Symmetry

Heating usually destroys quantum entanglement. We show that thermalization constrained to a non-Abelian strong-symmetry sector can instead generate a distillable resource that diverges with system size. In an exactly solvable local dimer chain, entanglement across an equal bipartition is exactly zero at $T=0$, whereas every fixed $T>0$ yields $E_D=\frac12\log_2 N+C(T)+o(1)$. Measurements of the two half-chain representation labels convert thermally populated non-Abelian sectors into standard ebits. More generally, for global-singlet thermal states of finite-range, uniformly bounded, locally $SU(2)$-invariant chains, there is a nonzero high-temperature interval in which the protocol yield satisfies $Y_N=\frac12\log_2 N+O_\beta(1)$ and $E_D\geq Y_N$. For the dimer chain, the full finite-size onset is governed by a universal Bessel-function crossover with $T_*(N)=\Delta/[\ln N+O(1)]$. Exact diagonalization of a frustrated $J_1$-$J_2$ chain shows the expected finite-size signatures. Thus thermal fluctuations can create entanglement across a macroscopic cut and convert it into an unbounded operational quantum resource.

quant-ph↗
arXiv2026

Certifying Nonclassical Proper-Time Histories with a Quantum Clock

Quantum clocks can acquire relativistic phases from motional or gravitational proper-time differences, but reduced clock dephasing alone does not certify nonclassical proper-time histories. We formulate this distinction as a channel-certification problem. First, we show that any two-level single-time dephasing signal, including one generated by an effective quantum proper-time label, admits a classical random proper-time representation. We then define the convex set of classical mixtures of experimentally specified proper-time histories and prove a Choi-rank separation criterion for conditioned coherent history recombination. A two-branch Ramsey protocol gives explicit bright- and dark-port population witnesses outside this classical set. The certification is operational and relative to the specified history set: it rules out classical mixtures of the same implemented proper-time histories, not arbitrary classical protocols with different histories or controls.

quant-ph↗
arXiv2026

The Exact Replica Threshold for Nonlinear Moments of Quantum States

Joint measurements on multiple copies of a quantum state provide access to nonlinear observables such as $\operatorname{tr}(\rho^t)$, but whether replica number marks a sharp information-theoretic resource boundary has remained unclear. For every fixed order $t\ge 3$, existing protocols show that $\lceil t/2\rceil$ replicas already suffice for polynomial-sample estimation of $\operatorname{tr}(\rho^t)$, yet it has remained open whether one fewer replica must necessarily incur a sample-complexity barrier growing with the dimension. We prove that this is indeed the case in the sample/copy-access model with replica-limited joint measurements: any protocol restricted to $\lceil t/2\rceil-1$ replicas requires dimension-growing sample complexity, while $\lceil t/2\rceil$ replicas suffice by prior work. Thus the exact replica threshold for fixed-order pure moments is $\lceil t/2\rceil$. Equivalently, for fixed-order pure moments, one additional coherent replica is not merely useful but marks the exact threshold between polynomial-sample estimation and a dimension-growing regime in the replica-limited model. We further show that the same threshold law extends to a broad family of observable-weighted moments $\operatorname{tr}(O\rho^t)$, including Pauli observables and other observables with bounded operator norm and macroscopic trace norm. Coherent replica number therefore acts as a genuinely discrete resource for nonlinear quantum-state estimation.

quant-ph↗
arXiv2026

Stone-in-Waiting: A Cloud-Based Accelerator for the Quantum Approximate Optimization Algorithm

The Quantum Approximate Optimization Algorithm (QAOA) and its advanced variant, the Quantum Alternating Operator Ansatz (QAOA), are major research topics in the current era of Noisy Intermediate-Scale Quantum (NISQ) computing. However, the problem of initializing their parameters remains unresolved. Motivated by the combinatorial optimization task in the 6th MindSpore Quantum Computing Hackathon (2024), this paper proposes Stone-in-Waiting, a cloud-based accelerator for obtaining high-quality initial parameters for QAOA. Internally, the accelerator builds on state-of-the-art theories and methods for parameter determination and integrates four self-developed algorithms for QAOA parameter initialization, mainly based on Bayesian methods, nearest-neighbor methods, and metric learning. Compared with the Baseline Algorithm, the generated parameters improve the score by 40.19%. Externally, the accelerator offers both a web interface and an API, providing flexible and convenient access for users to test and develop related experiments and applications. This paper presents the design principles and methods of Stone-in-Waiting, demonstrates its functional characteristics, compares the strengths and weaknesses of the four proposed algorithms, and validates the overall system performance through experiments.

quant-ph↗
arXiv2026

Antenna Array Beamforming Based on a Hybrid Quantum Optimization Framework

This paper proposes a hybrid quantum optimization framework for large-scale antenna-array beamforming with jointly optimized discrete phases and continuous amplitudes. The method combines quantum-inspired search with classical gradient refinement to handle mixed discrete-continuous variables efficiently. For phase optimization, a Gray-code and odd-combination encoding scheme is introduced to improve robustness and avoid the complexity explosion of higher-order Ising models. For amplitude optimization, a geometric spin-combination encoding and a two-stage strategy are developed, using quantum-inspired optimization for coarse search and gradient optimization for fine refinement. To enhance solution diversity and quality, a rainbow quantum-inspired algorithm integrates multiple optimizers for parallel exploration, followed by hierarchical-clustering-based candidate refinement. In addition, a double outer-product method and an augmented version are proposed to construct the coupling matrix and bias vector efficiently, improving numerical precision and implementation efficiency. Under the scoring rules of the 7th National Quantum Computing Hackathon, simulations on a 32-element antenna array show that the proposed method achieves a score of 461.58 under constraints on near-main-lobe sidelobes, wide-angle sidelobes, beamwidth, and optimization time, nearly doubling the baseline score. The proposed framework provides an effective reference for beamforming optimization in future wireless communication systems.

quant-ph↗
arXiv2026

Block-QAOA-Aware Detection with Parameter Transfer for Large-Scale MIMO

Large-scale MIMO detection remains challenging because exact or near-maximum-likelihood search is difficult to scale, while available quantum resources are insufficient for directly solving full-size detection instances by QAOA. This paper therefore proposes a Block-QAOA-Aware MIMO Detector (BQA-MD), whose primary purpose is to reorganize the detection chain so that it becomes compatible with limited-qubit local quantum subproblems. Specifically, BQA-MD combines block-QAOA-aware preprocessing in the QR domain, a standards-consistent blockwise 5G NR Gray-HUBO interface, an MMSE-induced dynamic regularized blockwise objective, and K-best candidate propagation. Within this framework, fixed-size block construction gives every local subproblem a uniform circuit width and parameter dimension, which in turn enables parameter-transfer QAOA as a practical realization strategy for structurally matched local subproblems. Experiments are conducted on a 16x16 Rayleigh MIMO system with 16QAM using classical simulation of the quantum subroutine. The results show that the regularized blockwise detector improves upon its unregularized counterpart, validating the adopted blockwise objective and the block-QAOA-aware design rationale. They also show that the parameter-transfer QAOA detector nearly matches the regularized blockwise exhaustive reference and clearly outperforms direct-training QAOA in BER, thereby supporting parameter reuse as the preferred QAOA realization strategy within the proposed framework. In the tested setting, MMSE remains slightly better in the low-SNR region, whereas the parameter-transfer QAOA detector becomes highly competitive from the medium-SNR regime onward.

quant-ph↗
arXiv2025

Leveraging Group Relative Policy Optimization to Advance Large Language Models in Traditional Chinese Medicine

Traditional Chinese Medicine (TCM) presents a rich and structurally unique knowledge system that challenges conventional applications of large language models (LLMs). Although previous TCM-specific LLMs have shown progress through supervised fine-tuning, they often face limitations in alignment, data quality, and evaluation consistency. In this study, we introduce Ladder-base, the first TCM-focused LLM trained with Group Relative Policy Optimization (GRPO), a reinforcement learning method that improves reasoning and factual consistency by optimizing response selection based on intra-group comparisons. Ladder-base is built upon the Qwen2.5-7B-Instruct foundation model and trained exclusively on the textual subset of the TCM-Ladder benchmark, using 80 percent of the data for training and the remaining 20 percent split evenly between validation and test sets. Through standardized evaluation, Ladder-base demonstrates superior performance across multiple reasoning metrics when compared to both state-of-the-art general-purpose LLMs such as GPT-4, Gemini 2.5, Claude 3, and Qwen3 and domain-specific TCM models including BenTsao, HuatuoGPT2, and Zhongjing. These findings suggest that GRPO provides an effective and efficient strategy for aligning LLMs with expert-level reasoning in traditional medical domains and supports the development of trustworthy and clinically grounded TCM artificial intelligence systems.

cs.CL↗
arXiv2025

TCM-Ladder: A Benchmark for Multimodal Question Answering on Traditional Chinese Medicine

Traditional Chinese Medicine (TCM), as an effective alternative medicine, has been receiving increasing attention. In recent years, the rapid development of large language models (LLMs) tailored for TCM has highlighted the urgent need for an objective and comprehensive evaluation framework to assess their performance on real-world tasks. However, existing evaluation datasets are limited in scope and primarily text-based, lacking a unified and standardized multimodal question-answering (QA) benchmark. To address this issue, we introduce TCM-Ladder, the first comprehensive multimodal QA dataset specifically designed for evaluating large TCM language models. The dataset covers multiple core disciplines of TCM, including fundamental theory, diagnostics, herbal formulas, internal medicine, surgery, pharmacognosy, and pediatrics. In addition to textual content, TCM-Ladder incorporates various modalities such as images and videos. The dataset was constructed using a combination of automated and manual filtering processes and comprises over 52,000 questions. These questions include single-choice, multiple-choice, fill-in-the-blank, diagnostic dialogue, and visual comprehension tasks. We trained a reasoning model on TCM-Ladder and conducted comparative experiments against nine state-of-the-art general domain and five leading TCM-specific LLMs to evaluate their performance on the dataset. Moreover, we propose Ladder-Score, an evaluation method specifically designed for TCM question answering that effectively assesses answer quality in terms of terminology usage and semantic expression. To the best of our knowledge, this is the first work to systematically evaluate mainstream general domain and TCM-specific LLMs on a unified multimodal benchmark. The datasets and leaderboard are publicly available at https://tcmladder.com and will be continuously updated.

cs.CL↗
arXiv2024

Hardness-Aware Scene Synthesis for Semi-Supervised 3D Object Detection

3D object detection aims to recover the 3D information of concerning objects and serves as the fundamental task of autonomous driving perception. Its performance greatly depends on the scale of labeled training data, yet it is costly to obtain high-quality annotations for point cloud data. While conventional methods focus on generating pseudo-labels for unlabeled samples as supplements for training, the structural nature of 3D point cloud data facilitates the composition of objects and backgrounds to synthesize realistic scenes. Motivated by this, we propose a hardness-aware scene synthesis (HASS) method to generate adaptive synthetic scenes to improve the generalization of the detection models. We obtain pseudo-labels for unlabeled objects and generate diverse scenes with different compositions of objects and backgrounds. As the scene synthesis is sensitive to the quality of pseudo-labels, we further propose a hardness-aware strategy to reduce the effect of low-quality pseudo-labels and maintain a dynamic pseudo-database to ensure the diversity and quality of synthetic scenes. Extensive experimental results on the widely used KITTI and Waymo datasets demonstrate the superiority of the proposed HASS method, which outperforms existing semi-supervised learning methods on 3D object detection. Code: https://github.com/wzzheng/HASS.

cs.CV↗
arXiv2023

On double Danielewski varieties

In this paper, we study the double Danielewski varieties which arose from the research on the classical Cancellation Problem. We describe the Makar-Limanov invariant and locally nilpotent derivations of these varieties. And in a subsequent paper we will describe the automorphisms groups of the varieties and verify that the varieties are counterexamples to the Cancellation Problem.

math.AG↗
arXiv2021

$δ$-$J$-ideals of commutative rings

Let $\mathcal{I}(R)$ be the set of all ideals of a ring $R$, $δ$ be an expansion function of $\mathcal{I}(R)$. In this paper, the $δ$-$J$-ideal of a commutative ring is defined, that is, if $a, b\in R$ and $ab\in I\in \mathcal{I}(R)$, then $a\in J(R)$ (the Jacobson radical of $R$) or $b\in δ(I)$. Moreover, some properties of $δ$-$J$-ideals are discussed,such as localizations, homomorphic images, idealization and so on.

math.AC↗