arXiv subjects

Dong An

Publications and source records attributed to Dong An.

At least 19 recordsLinked to original sources

arXiv2026

A quantum-assisted framework for PDE-based Bayesian inverse problems

Quantum computing offers potential advantages for solving partial differential equations (PDEs). However, most existing quantum PDE solvers primarily focus on preparing quantum states for solutions, while the efficient recovery of classical information from these states remains less explored. Motivated by the readout limitation, we propose a quantum-classical hybrid framework for Bayesian PDE inversion problems: The quantum processor evolves the PDE and evaluate the loss function with sampling noises, while the classical computer tunes the hyper-parameters in the Gaussian Process Regression to explore the next trial candidate. To match the quantum solvers for linear and semi-linear autonomous evolution PDEs, we suggest to use a normalized quantum-state loss as the data-misfit function and evaluate the new misfit by combining quantum PDE solvers with the Hadamard test, thereby allowing us to extract useful classical information using only a limited number of quantum state copies without reconstructing the full solution vector. The analysis of error propagation and overall complexity of loss evaluation under a prescribed accuracy shows that the new data-misfit function outperforms the conventional L2-loss under quantum measurements. Quantum circuit simulations of 1D and 2D linear convection diffusion equations under approximate and finite sampling loss evaluations, together with classical numerical experiments on a nonlinear forced viscous Burgers equation, demonstrate the feasibility of the proposed approach for parameter inversion even when the loss evaluations are affected by sampling noise. This framework may provide a viable quantum-assisted scheme for PDE-based inverse problems and elucidate the potential of quantum PDE algorithms in addressing a complete quantum-to-end optimization stack.

math.NA↗

arXiv2026

Fast-forwarding quantum algorithms for weakly nonlinear dissipative differential equations and beyond

We study a fast-forwarded quantum algorithm for solving weakly nonlinear dissipative ordinary differential equations. Our approach is a combination of the Carleman embedding technique and the linear combination of Hamiltonian simulation algorithm for linearized systems with fast-forwarded scaling. The complexity of our algorithm does not explicitly depend on the evolution time $T$, thus greatly improving the previous state-of-the-art $\widetilde{\mathcal{O}}(\sqrt{T})$ to $\mathcal{O}(1)$, and any remaining time dependence enters through the output norm and forcing parameters. We rigorously analyze the performance of this approach by convergence guarantees of the Carleman embedding for time-dependent coefficient matrices and detailed complexity estimates, and improve the realization of the Carleman-embedding-based algorithms by simplifying the post-selection step. In addition, we perform a numerical study on differential equations beyond the weakly nonlinear case, and identify possibility of achieving fast-forwarding scaling for systems with stronger nonlinearity or linear non-resonant effect.

quant-ph↗

arXiv2026

Quantum simulation of slow analytic time-dependent Hamiltonians

We develop a quantum algorithm for slow analytic Hamiltonians $\widetilde H(t)=H(t/T)$ with $\|H(s)\|\leq\alpha$ that achieves nearly additive query complexity and low gate overhead. Our main technical contribution is a periodic Gevrey extension of $H(s)$, together with Fourier component decay and truncation bounds that enable an efficient finite-dimensional simulation. Combined with Floquet embedding and optimal time-independent Hamiltonian simulation technique, this gives query complexity $\widetilde{\mathcal O}\!\left(\alpha T+\log(1/\varepsilon)\right)$ and additional gate complexity $\widetilde{\mathcal O}\!\left((\alpha T+\log(1/\varepsilon))^2\log(1/\varepsilon)\right)$, assuming coherent access to $H'(s)$ and endpoint derivatives. For slow analytic control Hamiltonians, only block encodings of the time-independent control operators are required, with the same query complexity and lower gate overhead. Our method also extends to Gevrey Hamiltonians and improves the precision dependence for simulating slow analytic semi-dissipative linear differential equations.

quant-ph↗

arXiv2026

Fast Nondestructive Readout for High-Clock-Rate Atom Array Quantum Processor

Neutral-atom arrays have rapidly advanced to support thousands of qubits and execute high-fidelity logical operations. However, these processors remain severely throttled by their slowest fundamental operation: nondestructive qubit measurement, which requires milliseconds and fundamentally limits the system's clock rate. This bottleneck arises from both an inherent photon-budget dilemma---sufficient fluorescence for reliable state discrimination must be collected without excessive heating or loss---and frame-based imaging, which imposes one common exposure and decision latency on intrinsically independent, site-local measurements. Here, we overcome these limitations with a fast, nondestructive readout architecture based on real-time, site-resolved adaptive protection. By integrating continuous photon counting with a dynamic feedforward framework, we decode qubit states with sub-microsecond latency and instantly shield atoms from redundant scattering. Demonstrated in parallel across a 100-qubit reconfigurable atom array, with adaptive protection on a 25-site subarray, this dynamic decision protocol reduces the average probe time to just $15\ \mu\text{s}$. Model-free benchmarking yields a discrimination infidelity of $4.1 \times 10^{-5}$ and an atom loss of $2.1 \times 10^{-4}$, simultaneously setting new performance records for atom arrays. Exploiting this capability, we operate repeated quantum circuits at an unprecedented 1.7 kHz clock rate with atoms reused over 120 consecutive rounds---nearly sevenfold higher than the previous record---and enter the sub-millisecond cycle regime for the first time. By removing nondestructive readout as the dominant cycle-time bottleneck, this work unlocks high-clock-rate mid-circuit syndrome extraction, paving the way for high-throughput, fault-tolerant quantum computation.

quant-ph↗

arXiv2026

FlowWAM: Optical Flow as a Unified Action Representation for World Action Models

World Action Models (WAMs) are able to leverage pretrained video generators for both world modeling and action prediction. However, directly leveraging such video generators for control raises a new challenge: how to represent actions in a suitable form that aligns with pretrained video generators while carrying enough motion cues for accurate control. Existing numerical actions fail to satisfy the former, and prior visual action representations overlook the temporal motion structure across frames. We address this issue with FlowWAM, a dual-stream diffusion framework that adopts optical flow as a unified, video-native action representation. Flow videos share the same format as RGB videos and encode rich per-pixel displacement. By jointly modeling them within a shared pretrained video generator, FlowWAM can naturally implement two modes of WAMs. In policy mode, FlowWAM generates flow for action prediction, while in world-model mode, it uses target flow sequences to guide future video generation. Moreover, since flow can be easily extracted from raw videos without action labels, FlowWAM can leverage large-scale action-unlabeled video datasets for pretraining. We empirically find that our flow-based action representation delivers gains across both modes. On RoboTwin manipulation, FlowWAM raises the success rate to 92.94% on the Clean setting and 92.14% on Random, outperforming both VLA and WAM baselines. On WorldArena world modeling, it achieves the best overall EWMScore (63.71) with an 18.4% relative improvement in trajectory accuracy. More results can be found on our project website: https://flow-wam.github.io .

cs.RO↗

arXiv2026

Quantum simulation of real-world nonlinear dynamics via Koopman method

Nonlinear dynamics is ubiquitous in nature, ranging from chemical pattern formation to ocean circulation, yet its simulation on quantum computers is fundamentally limited by the unitary nature of quantum evolution. We propose the quantum Koopman method, a data-driven framework that embeds nonlinear dynamics into a learned linear representation and implements the resulting evolution using shallow quantum circuits. This method learns Koopman observables from trajectory data, projects the lifted dynamics onto a finite-dimensional subspace, and decomposes the corresponding non-unitary propagator into parallel spectral channels. We utilize the Koopman method on a superconducting processor to simulate three distinct nonlinear systems, comprising reaction-diffusion dynamics, fluid motion on a sphere, and satellite-derived observations of Gulf Stream currents, employing up to 32 parallel circuits of 10 qubits. These quantum simulations capture the dominant multiscale patterns and statistical signatures of the underlying dynamics, and reveal a transition from performance limited by hardware noise in weakly nonlinear systems to performance limited by finite-dimensional Koopman representations as nonlinear scale interactions increase. This transition identifies a practical boundary for quantum-amenable nonlinear dynamics, establishing a hardware-validated route for simulating moderately nonlinear dynamics on near-term quantum hardware.

quant-ph↗

arXiv2026

Linear Combination of Hamiltonian Simulation with Commutator Scaling

The Linear Combination of Hamiltonian Simulation (LCHS) framework simulates dissipative linear dynamics by representing time evolution as an integral over unitary operators, which is discretized by quadrature and implemented via Hamiltonian simulation. While existing analyses achieve near-optimal scaling in time and precision using norm-based quantities of the dissipative generator, we show that implementing the Hamiltonian simulation steps with Multi-Product Formulas (MPFs) yields commutator-sensitive error and complexity bounds. We demonstrate that the quadrature rule affects not only discretization error but also commutator structure and query complexity. This dependence is quantified through post-quadrature analysis for abstract MPF error profiles and for general time-independent and local Hamiltonians using known commutator-sensitive MPF error estimates. We compare uniform trapezoidal and free-scale sinh--sinh quadrature, showing improved quadrature-cardinality scaling for the latter, and illustrate the framework with applications to fractional diffusion, advection--diffusion, and open quantum systems.

quant-ph↗

arXiv2026

Pauli-structured preconditioning for quantum linear system solvers

Preconditioning is a fundamental technique for accelerating classical linear system solvers, and understanding when its benefits persist in quantum linear system (QLS) solvers is important for assessing the practical resource requirements of quantum linear algebra. In QLS algorithms, however, the potential advantage of preconditioning may be offset by the normalization overhead incurred by composing separate block-encodings of the system matrix and the preconditioner, as observed in recent work. This limitation leaves open whether additional algebraic structure can make preconditioning effective in quantum access models. Motivated by this question, we show that Pauli-structured representations of both the system matrix and the preconditioner allow the preconditioned operator to be accessed through regrouped Pauli expansions. In this setting, algebraic regrouping of Pauli products can reduce the Pauli coefficient weight of the preconditioned operator, thereby altering the normalization parameters relevant to quantum algorithms. We derive explicit size and coefficient-weight bounds for the regrouped Pauli representations, and we trace their consequences for both direct block-encoding constructions and randomized Pauli linear system solvers. These results identify when Pauli-structured preconditioning can reduce the effective complexity parameters of QLS algorithms, rather than merely improving the classical condition number. Numerical experiments on a finite-dimensional synthetic benchmark show reductions in norm-aware direct block-encoding diagnostics and in the randomized QLS per-sample depth proxy.

quant-ph↗

arXiv2026

InfoQuant: Shaping Activation Distributions for Low-Bit LLM Quantization

Low-bit activation quantization remains a major bottleneck in efficient large language model (LLM) deployment. The difficulty is not only that activations contain outliers, but that their distributions are often poorly matched to a low-bit uniform quantizer. Existing post-training quantization (PTQ) methods suppress peaks, balance channels, or minimize reconstruction error, yet they rarely specify what activation distribution is actually easy to discretize. As a result, activations may appear numerically smoother while still incurring large quantization error because the quantization range remains wide or most values collapse into a few levels near the mean. We recast activation transformation as quantizer-facing distribution design and analyze quantization error from an information-theoretic perspective. Our analysis shows that quantization-friendly activations should jointly have a smaller numerical range and sufficient dispersion within that range. Guided by this analysis, we propose InfoQuant, a train-free method that employs Peak Suppression Orthogonal Transformation (PSOT) to shape activations into more quantization-friendly distributions. We further introduce adaptive outlier-token selection to improve the robustness of PSOT during optimization. Across multiple LLM families, InfoQuant consistently outperforms prior PTQ and end-to-end training baselines. Under W4A4KV4, it preserves 97% of floating-point accuracy on average and reduces the LLaMA-2 13B performance gap by 42% over the previous state of the art. Code is available at [https://github.com/LLIKKE/InfoQuant](https://github.com/LLIKKE/InfoQuant)

cs.LG↗

arXiv2026

Constant Factor Analysis of Optimal Quantum Linear Solvers in Practice

Optimal quantum linear equation solvers provide complexity $O(\kappa\log(1/\epsilon))$, where $\kappa$ is the condition number and $\epsilon$ is the allowable error. The optimal solver using a discrete adiabatic approach [PRX Quantum 3, 040303 (2022)] has large analytically proven constant factors for the upper bound on the complexity. The constant factors were later found to be about 1,200 times smaller in numerical testing [Quantum 9, 1887 (2025)]. This meant it is about an order of magnitude more efficient than using a randomised approach from [PRX Quantum 6, 040373 (2025)], which has far smaller analytically proven constant factors. Recently, a ``Shortcut'' method has been found to provide an optimal solver which also has small proven constant factors. In the present work, we conduct a comprehensive numerical analysis comparing this method with the adiabatic solver for two families of random linear systems. We find that, in the case where the solution norm is unknown, the adiabatic solver provides slightly better performance. If the solution norm is known, then the shortcut method provides significantly better performance for non-Hermitian matrices.

quant-ph↗

arXiv2026

LatentPilot: Scene-Aware Vision-and-Language Navigation by Dreaming Ahead with Latent Visual Reasoning

Existing vision-and-language navigation (VLN) models primarily reason over past and current visual observations, while largely ignoring the future visual dynamics induced by actions. As a result, they often lack an effective understanding of the causal relationship between actions and how the visual world changes, limiting robust decision-making. Humans, in contrast, can imagine the near future by leveraging action-dynamics causality, which improves both environmental understanding and navigation choices. Inspired by this capability, we propose LatentPilot, a new paradigm that exploits future observations during training as a valuable data source to learn action-conditioned visual dynamics, while requiring no access to future frames at inference. Concretely, we propose a flywheel-style training mechanism that iteratively collects on-policy trajectories and retrains the model to better match the agent's behavior distribution, with an expert takeover triggered when the agent deviates excessively. LatentPilot further learns visual latent tokens without explicit supervision; these latent tokens attend globally in a continuous latent space and are carried across steps, serving as both the current output and the next input, thereby enabling the agent to dream ahead and reason about how actions will affect subsequent observations. Experiments on R2R-CE, RxR-CE, and R2R-PE benchmarks achieve new SOTA results, and real-robot tests across diverse environments demonstrate LatentPilot's superior understanding of environment-action dynamics in scene. Project page:https://abdd.top/latentpilot/

cs.CV↗

arXiv2026

Achieving double-logarithmic precision dependence in optimization-based quantum unstructured search

Grover's algorithm is a fundamental quantum algorithm that achieves a quadratic speedup for unstructured search problems of size $N$. Recent studies have reformulated this task as a maximization problem on the unitary manifold and solved it via linearly convergent Riemannian gradient ascent (RGA) methods, resulting in a complexity of $O(\sqrt{N/M}\log (1/\varepsilon))$, where $M$ denotes the number of target items and $\varepsilon$ denotes the success probability error. In this work, we adopt the Riemannian modified Newton (RMN) method to solve the quantum search problem, under the assumption that the ratio $ M/N$ is known. We show that, in this setting, the Riemannian Newton direction is collinear with the Riemannian gradient in the sense that the Riemannian gradient is always an eigenvector of the corresponding Riemannian Hessian. This structure removes the overhead of Hessian inversion and allows the proposed RMN method to retain the local quadratic convergence in terms of the error $\varepsilon$. More precisely, we rigorously prove an overall complexity of $O(\sqrt{N/M}+\log\log(1/\varepsilon))$. Furthermore, our approach remains Grover-compatible, namely, it relies exclusively on the standard Grover diffusion and oracle operators to ensure algorithmic implementability, and its parameter update process can be efficiently precomputed on classical computers.

quant-ph↗

arXiv2026

FloorPlan-VLN: A New Paradigm for Floor Plan Guided Vision-Language Navigation

Existing Vision-Language Navigation (VLN) task requires agents to follow verbose instructions, ignoring some potentially useful global spatial priors, limiting their capability to reason about spatial structures. Although human-readable spatial schematics (e.g., floor plans) are ubiquitous in real-world buildings, current agents lack the cognitive ability to comprehend and utilize them. To bridge this gap, we introduce \textbf{FloorPlan-VLN}, a new paradigm that leverages structured semantic floor plans as global spatial priors to enable navigation with only concise instructions. We first construct the FloorPlan-VLN dataset, which comprises over 10k episodes across 72 scenes. It pairs more than 100 semantically annotated floor plans with Matterport3D-based navigation trajectories and concise instructions that omit step-by-step guidance. Then, we propose a simple yet effective method \textbf{FP-Nav} that uses a dual-view, spatio-temporally aligned video sequence, and auxiliary reasoning tasks to align observations, floor plans, and instructions. When evaluated under this new benchmark, our method significantly outperforms adapted state-of-the-art VLN baselines, achieving more than a 60\% relative improvement in navigation success rate. Furthermore, comprehensive noise modeling and real-world deployments demonstrate the feasibility and robustness of FP-Nav to actuation drift and floor plan distortions. These results validate the effectiveness of floor plan guided navigation and highlight FloorPlan-VLN as a promising step toward more spatially intelligent navigation.

cs.RO↗

arXiv2026

Efficient Quantum Simulation for Nonlinear Stochastic Differential Equations

Nonlinear stochastic differential equations (NSDEs) are a pillar of mathematical modeling for scientific and engineering applications. Accurate and efficient simulation of large-scale NSDEs is prohibitive on classical computers due to the large number of degrees of freedom, and it is challenging on quantum computers due to the linear and unitary nature of quantum mechanics. We develop a quantum algorithm to tackle nonlinear differential equations driven by the Ornstein-Uhlenbeck (OU) stochastic process. The query complexity of our algorithm scales logarithmically with the error tolerance and nearly quadratically with the simulation time. Our algorithmic framework comprises probabilistic Carleman linearization (PCL) to tackle nonlinearity coupled with stochasticity, and stochastic linear combination of Hamiltonian simulations (SLCHS) to simulate stochastic non-unitary dynamics. We obtain probabilistic exponential convergence for the Carleman linearization of Liu et al. [1], provided the NSDE is stable and reaches a steady state. We extend deterministic LCHS to stochastic linear differential equations, retaining near-optimal parameter scaling from An et al. [2] except for the nearly quadratic time scaling. This is achieved by using Monte Carlo integration for time discretization of both the stochastic inhomogeneous term in LCHS and the truncated Dyson series for each Hamiltonian simulation.

quant-ph↗

arXiv2026

Quantum circuit design from a retraction-based Riemannian optimization framework

Designing quantum circuits for ground state preparation is a fundamental task in quantum information science. However, standard Variational Quantum Algorithms (VQAs) are often constrained by limited ansatz expressivity and difficult optimization landscapes. To address these issues, we adopt a geometric perspective, formulating the problem as the minimization of an energy cost function directly over the unitary group. We establish a retraction-based Riemannian optimization framework for this setting, ensuring that all algorithmic procedures are implementable on quantum hardware. Within this framework, we unify existing randomized gradient approaches under a Riemannian Random Subspace Gradient Projection (RRSGP) method. While recent geometric approaches have predominantly focused on such first-order gradient descent techniques, efficient second-order methods remain unexplored. To bridge this gap, we derive explicit expressions for the Riemannian Hessian and show that it can be estimated directly on quantum hardware via parameter-shift rules. Building on this, we propose the Riemannian Random Subspace Newton (RRSN) method, a scalable second-order algorithm that constructs a Newton system from measurement data. Numerical simulations indicate that RRSN achieves quadratic convergence, yielding high-precision ground states in significantly fewer iterations compared to both existing first-order approaches and standard VQA baselines. Ultimately, this work provides a systematic foundation for applying a broader class of efficient Riemannian algorithms to quantum circuit design.

quant-ph↗

arXiv2026

Lemon Agent Technical Report

Recent advanced LLM-powered agent systems have exhibited their remarkable capabilities in tackling complex, long-horizon tasks. Nevertheless, they still suffer from inherent limitations in resource efficiency, context management, and multimodal perception. Based on these observations, Lemon Agent is introduced, a multi-agent orchestrator-worker system built on a newly proposed AgentCortex framework, which formalizes the classic Planner-Executor-Memory paradigm through an adaptive task execution mechanism. Our system integrates a hierarchical self-adaptive scheduling mechanism that operates at both the overall orchestrator layer and workers layer. This mechanism can dynamically adjust computational intensity based on task complexity. It enables orchestrator to allocate one or more workers for parallel subtask execution, while workers can further improve operational efficiency by invoking tools concurrently. By virtue of this two-tier architecture, the system achieves synergistic balance between global task coordination and local task execution, thereby optimizing resource utilization and task processing efficiency in complex scenarios. To reduce context redundancy and increase information density during parallel steps, we adopt a three-tier progressive context management strategy. To make fuller use of historical information, we propose a self-evolving memory system, which can extract multi-dimensional valid information from all historical experiences to assist in completing similar tasks. Furthermore, we provide an enhanced MCP toolset. Empirical evaluations on authoritative benchmarks demonstrate that our Lemon Agent can achieve a state-of-the-art 91.36% overall accuracy on GAIA and secures the top position on the xbench-DeepSearch leaderboard with a score of 77+.

cs.MA↗

arXiv2026

Ensemble-Based Quantum Signal Processing for Error Mitigation

Despite rapid advances in quantum hardware, noise remains a central obstacle to deploying quantum algorithms on near-term devices. In particular, random coherent errors that accumulate during circuit execution constitute a dominant and fundamentally challenging noise source. We introduce a noise-resilient framework for Quantum Signal Processing (QSP) that mitigates such coherent errors without increasing circuit depth or ancillary qubit requirements. Our approach uses ensembles of noisy QSP circuits combined with measurement-level averaging to suppress random phase errors in Z rotations. Building on this framework, we develop robust QSP algorithms for implementing polynomial functions of Hermitian matrices and for estimating observables, with applications to Hamiltonian simulation, quantum linear systems, and ground-state preparation. We analyze the trade-off between approximation error and hardware noise, which is essential for practical implementation under the stringent depth and coherence constraints of current quantum hardware. Our results establish a practical pathway for integrating error mitigation seamlessly into algorithmic design, advancing the development of robust quantum computing, and enabling the discovery of scientific applications with near- and mid-term quantum devices.

quant-ph↗

arXiv2026

Contour-integral based quantum eigenvalue transformation: analysis and applications

Eigenvalue transformations appear ubiquitously in scientific computation, ranging from matrix polynomials to differential equations, and are beyond the reach of the quantum singular value transformation framework. In this work, we study the efficiency of quantum algorithms based on contour integral representation for eigenvalue transformations from both theoretical and practical aspects. Theoretically, we establish a complete complexity analysis of the contour integral approach proposed in [Takahira, Ohashi, Sogabe, and Usuda. Quant. Inf. Comput., 22, 11\&12, 965--979 (2021)]. Moreover, we combine the contour integral approach and the sampling-based linear combination of unitaries to propose a quantum algorithm for estimating observables of eigenvalue transformations using only $3$ additional qubits. Practically, we design contour integral based quantum algorithms for Hamiltonian simulation, matrix polynomials, and solving linear ordinary differential equations, and show that the contour integral algorithm can outperform all the existing quantum algorithms in the case of solving asymptotically stable differential equations.

quant-ph↗