arXiv subjects
Publications and source records attributed to Zhicheng Zhang.
In this paper, we construct the canonical basis for the modified mirabolic quantum $\mathfrak{sl}_n$. We then study the associated $\dot{U}_v(\mathfrak{sl}_n)$-module and $\dot{U}_v(\mathfrak{sl}_n)$-comodule structures and prove the positivity of this basis with respect to these two structures.
Endoscopic video contains state transitions induced by camera displacement, deformable tissue, and instrument interaction, yet existing pre-training methods treat dynamics implicitly. Inspired by action-conditioned joint-embedding predictive world models and by the observation that endoscopic optical flow contains both shared image-plane displacement and localized residual motion, we reformulate passive endoscopic video pre-training as causal motion-guided latent-state prediction. We present EndoWorld-JEPA, to our knowledge the first latent world-model pre-training framework designed for general-purpose endoscopic video representation learning. In place of recorded actions, calibrated poses, or robot kinematics, the model conditions prediction of the next latent state on motion observed up to the current state. Its Optical Motion-guided module separates dominant displacement from residual motion and converts the resulting evidence into an ordered temporal motion condition and spatial local-motion weights. Complementary global and motion-local predictors use these outputs: the temporal condition modulates both latent transitions, whereas the local weights define an auxiliary motion-local state that extends prediction from scene-level evolution to spatially selective dynamics. Patch-wise motion weighting emphasizes localized change while retaining anatomical context, and past-motion-window dropout randomly withholds the complete motion condition to reduce dependence on unreliable motion. This global--local formulation learns predictable visual--motion dynamics in representation space without reconstructing stochastic appearance artifacts. Evaluation shows that a common pre-trained checkpoint achieves strong transfer across four downstream benchmarks, supporting motion-guided global--local latent prediction as an effective pre-training paradigm for endoscopic video.
We have studied the vortex bound states of superconducting linear and quadratic Weyl semimetals with time reversal symmetry. For vortex with vorticity $n$ (vortex line along $z$ direction) and Weyl semimetals with Weyl point chirality $χ$, there are $\vert nχ\vert$ gapless vortex modes around the location of each Weyl point in superconducting Weyl semimetals. We show that the appearance of $\vert nχ\vert$ gapless vortex modes originates from the imbalanced pumping of flux bound states between Chern insulators obtained at $k_{z}$ and $-k_{z}$ in Weyl semimetals. Such a physical picture is verified by numerical calculations on lattice models. Moreover, the gapless modes around each Weyl point can be characterized by the second Chern number defined in a synthetic four-dimensional space based on the effective BdG Hamiltonian. Finally, these gapless vortex modes are found to be robust against rotational symmetry-breaking terms.
Practical quantum programs interleave quantum and classical computation: classical data shape the quantum operations that are performed, and measurement outcomes shape the classical computation that follows. Formal verification of such programs in a proof assistant requires mechanizing a program logic that handles this interplay consistently at every level, from the mathematics of quantum mechanics, through program syntax and semantics, to specifications and proof rules. Such mechanizations, along with the program proofs built on them, typically require substantial manual effort. We present QEDIA, a framework for verifying quantum programs with classical variables in Lean 4. At its foundation is an open library that formalizes the quantum Hoare logic QHL+ across all these levels and proves the logic sound for both partial and total correctness. We construct the library and the program proofs, under human supervision, using an LLM-based prover agent, whose general-purpose core we extend for quantum program verification. We illustrate QEDIA with verified programs including the quantum Fourier transform, phase estimation, repeat-until-success circuits, and Hamiltonian simulation.
We study the power of local test for bipartite quantum states. Our central result is that, for properties of bipartite pure states, unitary invariance on one part implies an \textit{optimal} (over all global testers) local tester acting only on the other part. As an application, we demonstrate - Purified samples offer no advantage in property testing of mixed states. - A matching lower bound $Ω(r^2/\varepsilon^2)$ for testing the Schmidt rank of bipartite states with perfect completeness, settling an open question raised in the survey of Montanaro and de Wolf (ToC 2016). - A lower bound $Ω((\sqrt{n}+\sqrt{r})\cdot\sqrt{r}/\varepsilon^2)$ for testing whether an $n$-partite state is a matrix product state of bond dimension $r$ or $\varepsilon$-far, improving the prior lower bounds $Ω(\sqrt{n}/\varepsilon^2)$ by Soleimanifar and Wright (SODA 2022) and $Ω(\sqrt{r})$ by Aaronson et al. (ITCS 2024). - A matching lower bound $Ω(d/\varepsilon^2)$ for testing whether a $d$-dimensional bipartite state is maximally entangled or $\varepsilon$-far, showing that the algorithm of O'Donnell and Wright (STOC 2015) is optimal for this task. - A query lower bound $\widetildeΩ(\sqrt{d/Δ})$ for the $d$-dimensional entanglement entropy problem with gap $Δ$, improving the prior lower bounds $Ω(\sqrt[4]{d})$ by She and Yuen (ITCS 2023) and $\widetildeΩ(1/\sqrtΔ)$ by Wang and Zhang (SICOMP 2025) and Weggemans (Quantum 2025). Moreover, we extend our central result to a robust version where the tested states are subject to noise and are not guaranteed to be pure: in this case, one-way LOCC is sufficient to realize the optimal tester.
We consider a fundamental task in quantum information theory, estimating the values of $tr(Oρ)$, $tr(Oρ^2)$, $\ldots$, $tr(Oρ^k)$ for an observable $O$ and a quantum state $ρ$. We show that $\widetildeΘ(k)$ samples of $ρ$ are sufficient and necessary to simultaneously estimate all the $k$ values. This means that estimating all the $k$ values is almost as easy as estimating only one of them, $tr(Oρ^k)$. As an application, our approach advances the sample complexity of entanglement spectroscopy and the virtual cooling for quantum many-body systems. Moreover, we extend our approach to estimating general functionals by polynomial approximation.
In this paper, we introduce a notion of abstract quantum data type within the framework of universal algebra. This notion provides an algebraic foundation for describing data abstraction in quantum programming. We formally define a quantisation of classical data types and show that their equational specifications can be soundly lifted to the quantum setting. Two standard quantisation methods for classical functions, namely the bit oracle and the phase oracle, arise as special cases of this general construction. We illustrate the framework with applications to quantum arrays and quantum error-correcting codes, showing how they can be understood through the lens of data-type quantisation. We further establish conditions under which quantisation preserves structural relationships and constructions of classical data types, including embeddings, isomorphisms, and products.
Large Language Models (LLMs) excel in stand-alone code tasks like HumanEval and MBPP, but struggle with handling entire code repositories. This challenge has prompted research on enhancing LLM-codebase interaction at a repository scale. Current solutions rely on similarity-based retrieval or manual tools and APIs, each with notable drawbacks. Similarity-based retrieval often has low recall in complex tasks, while manual tools and APIs are typically task-specific and require expert knowledge, reducing their generalizability across diverse code tasks and real-world applications. To mitigate these limitations, we introduce CodexGraph, a system that integrates LLM agents with graph database interfaces extracted from code repositories. By leveraging the structural properties of graph databases and the flexibility of the graph query language, CodexGraph enables the LLM agent to construct and execute queries, allowing for precise, code structure-aware context retrieval and code navigation. We assess CodexGraph using three benchmarks: CrossCodeEval, SWE-bench, and EvoCodeBench. Additionally, we develop five real-world coding applications. With a unified graph database schema, CodexGraph demonstrates competitive performance and potential in both academic and real-world environments, showcasing its versatility and efficacy in software engineering. Our application demo: https://github.com/modelscope/modelscope-agent/tree/master/apps/codexgraph_agent.
How many black-box queries to a quantum channel are needed to learn its full classical description? This question lies at the heart of quantum channel tomography (also known as quantum process tomography), a fundamental task in the characterization and validation of quantum hardware. Despite extensive prior work, the optimal query complexity for quantum channel tomography is far from fully understood. In this paper, we study tomography of an unknown quantum channel with input dimension $d_1$, output dimension $d_2$, and Kraus rank at most $r$, to within error $\varepsilon$. We identify the dilation rate $τ= r d_2 / d_1$ (which always satisfies $τ\geq 1$ due to the trace preservation of quantum channels) as a key parameter, and establish that the optimal query complexity of channel tomography exhibits distinct scaling laws across three regimes of $τ$. - In the boundary regime ($τ= 1$): we show that the query complexity is $Θ(r d_1 d_2/\varepsilon)$ for Choi trace norm error $\varepsilon$, and is upper bounded by $O(\min\{r d_1^{1.5} d_2/\varepsilon, r d_1 d_2/\varepsilon^2\})$ and lower bounded by $Ω(r d_1 d_2/\varepsilon)$ for diamond norm error $\varepsilon$. - In the away-from-boundary regime ($τ\geq 1+Ω(1)$): we show that the query complexity is $Θ(r d_1 d_2/\varepsilon^2)$ for both Choi trace norm and diamond norm errors $\varepsilon$. Our results uncover a sharp Heisenberg-to-classical phase transition in the query complexity of quantum channel tomography: at $τ=1$, the optimal query complexity exhibits Heisenberg scaling $1/\varepsilon$, whereas for $τ\geq 1+Ω(1)$, it exhibits classical scaling $1/\varepsilon^2$. In addition, we show that in the near-boundary regime ($1< τ< 1+o(1)$), the query complexity exhibits a mixture of Heisenberg and classical scaling behaviors.
We settle the problem of estimating the trace distance and (square root) fidelity between $n$-qubit pure quantum states to within additive error $\varepsilon$, given their independent samples, which was raised as an open question by Wang (IEEE Trans. Inf. Theory 2024). This is achieved by a quantum algorithm with optimal sample complexity $Θ(1/\varepsilon^2)$, improving the long-standing folklore with sample complexity $O(1/\varepsilon^4)$. At the heart of our algorithm is a samplized phase estimation of the product of two Householder reflections. This is realized by an improved (multi-)samplizer for pure states, through which any quantum query algorithm using $Q$ queries to the reflection operator $I - 2|ψ\rangle\!\langleψ|$ can be converted to a $δ$-close (in the diamond norm distance) quantum sample algorithm using $Θ(Q^2/δ)$ samples of the state $|ψ\rangle$. This samplizer for pure states is also shown to be optimal.
Hard negative mining has become the dominant strategy for training retrievers, yet it faces intrinsic limitations: negatives are bounded by corpus availability, selected by retriever score rather than diagnostic value, and increasingly contaminated by false positives as the retriever improves. LLM-based synthesis offers a principled alternative, where negatives that are unconstrained, targeted, and free from false positive risk. But we show that naively incorporating generated negatives into contrastive learning often degrades retrieval performance. We identify and formalize the root cause as a generative-discriminative gap: LLM generation optimizes for fluent, plausible text, while contrastive learning demands strategic violations of relevance at the decision boundary. Our analysis reveals two compounding failure modes: discriminative-agnostic generation, where the LLM lacks an explicit model of query information needs and defaults to generic or topic-drifted text that provides no contrastive signal; and source-dependent shortcuts, where distributional artifacts enable the model to distinguish negatives by origin rather than relevance, causing gradient drift that actively corrupts optimization. To close this gap, we propose CausalNeg consisting of two main modules: (1) CoT-guided counterfactual perturbation for data construction: decomposes why a document satisfies a query into explicit information requirements, then surgically violates individual requirements to construct negatives with controlled, interpretable hardness. (2) Query-view entropy maximization during training: disperses generated negatives across the similarity spectrum, minimizing the mutual information between source identity and similarity scores to suppress shortcut exploitation. We make our code publicly available at https://github.com/mzhangzhicheng/CausalNeg.
Audio-driven talking-head generation has advanced rapidly, yet existing evaluation protocols mainly rely on frame-wise metrics that assume strict temporal correspondence between generated and reference videos. This assumption does not match speech-driven facial motion, which naturally includes slight timing shifts, different speaking speeds, and stylistic variations. As a result, conventional metrics may treat harmless timing differences as quality errors, making it harder to fairly compare methods and understand their trade-offs. In this work, we argue that evaluation of dynamic generative models should be formulated as a sequence-alignment problem rather than independent frame comparison. We introduce a unified sequence-level reformulation that integrates Soft Dynamic Time Warping into established evaluation pipelines. By aligning feature trajectories while preserving temporal order, the proposed framework provides robustness to bounded temporal misalignments without altering the underlying perceptual, identity, or synchronization encoders. We show that frame-wise evaluation can be viewed as a special case under rigid alignment, while sequence-level alignment provides improved stability, lower sensitivity to timing differences, and clearer separation between modeling paradigms. Building on this principled formulation, we conduct a large-scale benchmark of 20 methods across seven datasets spanning canonical, in-the-wild, and style-diverse scenarios under standardized protocols. Extensive experiments show that temporally aligned metrics are more robust to timing differences, provide more consistent results across datasets, and better reveal systematic trade-offs between modeling paradigms, such as synchronization versus realism and expressiveness versus stability.
Audio-driven talking-head generation has achieved remarkable progress with recent models such as AniTalker, FLOAT, and Sonic. Despite their success, most existing approaches rely on a single static reference image to condition the entire video generation process at inference stage. This static conditioning paradigm often creates a mismatch between fixed identity features and dynamically evolving facial motion, leading to identity drift, temporal inconsistency, and degraded perceptual quality. We introduce Test-Time Self-Adaptive Conditioning (TT-SAC), a parameter-free inference framework that enables pretrained talking-head generators to adapt their conditioning representations during inference without retraining, gradient updates, or additional supervision. Instead of treating the reference portrait as immutable, TT-SAC composes the generator with its encoder in a feedback loop: the generator's own outputs are re-encoded to construct a refined conditioning representation that better aligns with the temporal dynamics of the synthesized sequence. A single adaptation step approximates a self-consistent equilibrium of the generative process, stabilizing identity and motion across time. We further provide theoretical analysis showing that test-time conditioning adaptation reduces feature variance and improves generative stability under mild Lipschitz assumptions, while exhibiting a principled bias-variance tradeoff that governs the optimal strength of adaptation. Extensive experiments on state-of-the-art talking-head generators and benchmark datasets demonstrate consistent improvements in lip-sync accuracy, temporal coherence, identity preservation, and perceptual fidelity. TT-SAC offers a model-agnostic and training-free strategy for enhancing generative video models, establishing test-time conditioning adaptation as an effective mechanism for stabilizing audio-driven portrait animation.
Blind image quality assessment (BIQA) for ultrahighdefinition (UHD) images remains challenging because native-resolution inference is computationally expensive, whereas aggressive resizing or isolated cropping may suppress scale-sensitive distortions and weaken the relationship between local artifacts and global scene context. This paper aims to improve UHD-BIQA by explicitly modeling the structural dependencies among sampled image regions rather than treating them as independent views, and a graph representation learning framework UHD-GCN-BIQA is proposed. The framework samples aspect-ratio-aligned patches from each UHD image, encodes them as graph nodes, and constructs a hybrid k-nearest-neighbor graph using spatial proximity and feature similarity. Residual graph convolution is used to propagate contextual information across regions, and gated attention pooling aggregates patchlevel evidence into an imagelevel quality prediction. An exponential moving average normalized multiobjective loss function is adopted to stabilize the joint optimization of regression, correlation, and ranking objectives. Experiments on the UHD-IQA benchmark show that UHD-GCN-BIQA achieves PLCC = 0.7784, SRCC = 0.8019, and RMSE = 0.0519, obtaining competitive correlation performance and the lowest RMSE among the compared methods. These results indicate that graph-based region relation modeling is effective for UHD image quality assessment, particularly for improving absolute quality score estimation under high-resolution visual content.
In this paper, we study second-order lag consensus in multi-agent cyber-physical networks subject to random noise and input failures, within a framework modeling the interactions and perceptions between physical twins and digital twins. We propose a lag consensus protocol and establish sufficient conditions for the mean-square (exponential) stability of the resulting stochastic lag error dynamics. The consensus criteria are derived via Lyapunov analysis using the Itô formula, ensuring robustness to random perturbations and intermittent input failures. Numerical examples illustrate the effectiveness of the proposed method.
We consider the problem of quantum channel certification to unitary, where one is given access to an unknown $d$-dimensional channel $\mathcal{E}$, and wants to test whether $\mathcal{E}$ is equal to a target unitary channel or is $\varepsilon$-far from it in the diamond norm. We present optimal quantum algorithms for this problem, settling the query complexities in three access models with increasing power. Specifically, we show that: (i) $Θ(d/\varepsilon^2)$ queries suffice for incoherent access model, matching the lower bound due to Fawzi, Flammarion, Garivier, and Oufkir (COLT 2023). (ii) $Θ(d/\varepsilon)$ queries suffice for coherent access model, matching the lower bound due to Regev and Schiff (ICALP 2008). (iii) $Θ(\sqrt{d}/\varepsilon)$ queries suffice for source-code access model, matching the lower bound due to Jeon and Oh (npj Quantum Inf. 2026). This demonstrates a strict hierarchy of complexities for quantum channel certification to unitary across various access models.
Omnimodal understanding entails a massive, highly redundant search space of cross-modal interactions, demanding focused and deliberative reasoning. Current reasoning paradigms rely on either sequential step-by-step generation or parallel sample-by-sample rollouts, leading to isolated reasoning trajectories. This inability to share promising intermediate paths severely limits exploration efficiency and causes compounding errors in complex audio-visual tasks. To break this bottleneck, we introduce Omni-o3, a novel framework driven by a deep nested deduction policy. By formulating reasoning as a dynamic recursive search, Omni-o3 inherently shares reasoning prefixes across branches, enabling the iterative execution of four atomic cognitive actions: expansion, selection, simulation, and backpropagation. To empower this framework, we propose a robust two-stage training paradigm: (1) cold-start supervised fine-tuning on 101K high-quality, long-chain trajectories distilled from 3.5M diverse omnimodal samples, enabling necessary recursive search patterns; and (2) nested group rollout-driven exploratory reinforcement learning on 18K complex multi-turn samples, explicitly guided by a novel multi-step reward model to stimulate deep nested reasoning. Extensive experiments demonstrate that Omni-o3 achieves competitive performance across 11 benchmarks, unlocking advanced capabilities in comprehensive audio-visual, visual-centric, and audio-centric reasoning tasks.
We present Wan-Image, a unified visual generation system explicitly engineered to paradigm-shift image generation models from casual synthesizers into professional-grade productivity tools. While contemporary diffusion models excel at aesthetic generation, they frequently encounter critical bottlenecks in rigorous design workflows that demand absolute controllability, complex typography rendering, and strict identity preservation. To address these challenges, Wan-Image features a natively unified multi-modal architecture by synergizing the cognitive capabilities of large language models with the high-fidelity pixel synthesis of diffusion transformers, which seamlessly translates highly nuanced user intents into precise visual outputs. It is fundamentally powered by large-scale multi-modal data scaling, a systematic fine-grained annotation engine, and curated reinforcement learning data to surpass basic instruction following and unlock expert-level professional capabilities. These include ultra-long complex text rendering, hyper-diverse portrait generation, palette-guided generation, multi-subject identity preservation, coherent sequential visual generation, precise multi-modal interactive editing, native alpha-channel generation, and high-efficiency 4K synthesis. Across diverse human evaluations, Wan-Image exceeds Seedream 5.0 Lite and GPT Image 1.5 in overall performance, reaching parity with Nano Banana Pro in challenging tasks. Ultimately, Wan-Image revolutionizes visual content creation across e-commerce, entertainment, education, and personal productivity, redefining the boundaries of professional visual synthesis.