arXiv subjects

Qian Zuo

Publications and source records attributed to Qian Zuo.

12 recordsLinked to original sources

arXiv2026

Numerical solution of the nonlinear Dirac equation by a splitting variational quantum algorithm

In this work, we propose an operator-splitting variational quantum algorithm, termed Dirac-sVQA, for simulating the nonlinear Dirac equation (NLDE). The main difficulty arises from the state-dependent nonlinear interaction, its time-discrete update depends explicitly on the intermediate spinor state and, in general, cannot be implemented as a fixed state-independent unitary circuit. To address this difficulty, we decompose the NLDE evolution into a structured linear Dirac substep and a nonlinear variational correction. The linear substep is implemented by a spinor-Fourier Dirac propagator on a joint position-spin register, preserving the spin-momentum coupling and mass-induced spin evolution of the Dirac operator. The nonlinear correction is reformulated as a measurement-based variational update through a small set of overlap, self-channel, and cross-channel observables. We provide the corresponding quantum circuits and derive measurement-aware resource and complexity estimates. Numerical experiments in several nonlinear regimes show that Dirac-sVQA accurately captures both the total density and the componentwise spinor dynamics, agrees well with classical Fourier pseudospectral splitting solutions, and exhibits stable error behavior over time. These results provide numerical evidence for the feasibility of operator-splitting variational quantum simulation for nonlinear relativistic wave equations.

quant-ph↗

arXiv2026

Planning Neural Dynamics with Lie Group Embedding through Supervised Projective Manifold Learning

We propose Lie group embedded dynamical neural networks (LieEDNN) and the corresponding learning algorithms based on gradient descent and metric projection on smooth manifold, where we treat Lie group as an intrinsic representation for continuous symmetry of manifold geometry. Thereby we achieve learnable and stable dynamics on the underlying manifold for general Lie group, and we are able to utilize the powerful representation capability of Lie group such as SO(3) and SE(3) to solve real world engineering problems in areas such as robotics, graphics, and control. Two core challenges are: (i) General Lie groups are incompatible with addition arithmetic, which is necessary for neural network interactions. (ii) The dynamics evolve in the nonlinear representation space of special algebra rather than the normal Euclidean space, which violates the paradigm of common neural ODEs. To address these two challenges, we firstly introduce adjoint Lie group action on the Lie algebra, which induces a linear mapping and transfer to the block-wise structure of weight matrices, such that addition could operate on the Lie algebra as a vector space. Then we parameterize the Lie algebra and the adjoint action as linear transformation so that the architecture is aligned with neural network perceptrons. Explicitly, this embedding appears as block-wise manifold constraints on weights, and we develop algorithms to learn the equilibrium with stability guarantees of the temporal neural network dynamics. Experiments are implemented on a specific Lie group SE(3), with the application scenario of telescopic manipulators.

cs.LG↗

arXiv2026

Integrating LTL Constraints into PPO for Safe Reinforcement Learning

This paper proposes Proximal Policy Optimization with Linear Temporal Logic Constraints (PPO-LTL), a framework that integrates safety constraints written in LTL into PPO for safe reinforcement learning. LTL constraints offer rigorous representations of complex safety requirements, such as regulations that broadly exist in robotics, enabling systematic monitoring of safety requirements. Violations against LTL constraints are monitored by limit-deterministic B\"uchi automata, and then translated by a logic-to-cost mechanism into penalty signals. The signals are further employed for guiding the policy optimization via the Lagrangian scheme. Extensive experiments on the Zones and CARLA environments show that our PPO-LTL can consistently reduce safety violations, while maintaining competitive performance, against the state-of-the-art methods. The code is at https://github.com/EVIEHub/PPO-LTL.

cs.LG↗

arXiv2026

Near-Constant Strong Violation and Last-Iterate Convergence for Online CMDPs via Decaying Safety Margins

We study safe online reinforcement learning in Constrained Markov Decision Processes (CMDPs) under strong regret and violation metrics, which forbid error cancellation over time. Existing primal-dual methods that achieve sublinear strong reward regret inevitably incur growing strong constraint violation or are restricted to average-iterate convergence due to inherent oscillations. To address these limitations, we propose the Flexible safety Domain Optimization via Margin-regularized Exploration (FlexDOME) algorithm, the first to provably achieve near-constant $\tilde{O}(1)$ strong constraint violation alongside sublinear strong regret and non-asymptotic last-iterate convergence. FlexDOME incorporates time-varying safety margins and regularization terms into the primal-dual framework. Our theoretical analysis relies on a novel term-wise asymptotic dominance strategy, where the safety margin is rigorously scheduled to asymptotically majorize the functional decay rates of the optimization and statistical errors, thereby clamping cumulative violations to a near-constant level. Furthermore, we establish non-asymptotic last-iterate convergence guarantees via a policy-dual Lyapunov argument. Experiments corroborate our theoretical findings.

cs.LG↗

arXiv2025

Anti-Disturbance Hierarchical Sliding Mode Controller for Deep-Sea Cranes with Adaptive Control and Neural Network Compensation

To address non-linear disturbances and uncertainties in complex marine environments, this paper proposes a disturbance-resistant controller for deep-sea cranes. The controller integrates hierarchical sliding mode control, adaptive control, and neural network compensation techniques. By designing a global sliding mode surface, the dynamic coordination between the driving and non-driving subsystems is achieved, ensuring overall system stability. The subsystem surfaces reduce oscillations and enhance tracking accuracy. Adaptive control dynamically adjusts system parameters, enhancing robustness against external uncertainties, while the neural network compensates for time-varying disturbances through real-time learning. The stability of the control scheme is verified on the basis of Lyapunov theory. The simulation results demonstrate that, compared to traditional PID control, the proposed controller exhibits significant advantages in trajectory tracking accuracy, response speed, and disturbance rejection.

eess.SY↗

arXiv2025

Ensuring Safety in an Uncertain Environment: Constrained MDPs via Stochastic Thresholds

This paper studies constrained Markov decision processes (CMDPs) with constraints against stochastic thresholds, aiming at safety of reinforcement learning in unknown and uncertain environments. We leverage a Growing-Window estimator sampling from interactions with the uncertain environment to estimate the thresholds, based on which we design Stochastic Pessimistic-Optimistic Thresholding (SPOT), a novel model-based primal-dual algorithm for multiple constraints against stochastic thresholds. SPOT enables reinforcement learning under both pessimistic and optimistic threshold settings. We prove that our algorithm achieves sublinear regret and constraint violation; i.e., a reward regret of $\tilde{\mathcal{O}}(\sqrt{T})$ while allowing an $\tilde{\mathcal{O}}(\sqrt{T})$ constraint violation over $T$ episodes. The theoretical guarantees show that our algorithm achieves performance comparable to that of an approach relying on fixed and clear thresholds. To the best of our knowledge, SPOT is the first reinforcement learning algorithm that realises theoretical guaranteed performance in an uncertain environment where even thresholds are unknown.

cs.LG↗

arXiv2023

Fast and Practical Quantum-Inspired Classical Algorithms for Solving Linear Systems

We propose fast and practical quantum-inspired classical algorithms for solving linear systems. Specifically, given sampling and query access to a matrix $A\in\mathbb{R}^{m\times n}$ and a vector $b\in\mathbb{R}^m$, we propose classical algorithms that produce a data structure for the solution $x\in\mathbb{R}^{n}$ of the linear system $Ax=b$ with the ability to sample and query its entries. The resulting $x$ satisfies $\|x-A^{+}b\|\leqε\|A^{+}b\|$, where $\|\cdot\|$ is the spectral norm and $A^+$ is the Moore-Penrose inverse of $A$. Our algorithm has time complexity $\widetilde{O}(κ_F^4/κε^2)$ in the general case, where $κ_{F} =\|A\|_F\|A^+\|$ and $κ=\|A\|\|A^+\|$ are condition numbers. Compared to the prior state-of-the-art result [Shao and Montanaro, arXiv:2103.10309v2], our algorithm achieves a polynomial speedup in condition numbers. When $A$ is $s$-sparse, our algorithm has complexity $\widetilde{O}(s κ\log(1/ε))$, matching the quantum lower bound for solving linear systems in $κ$ and $1/ε$ up to poly-logarithmic factors [Harrow and Kothari]. When $A$ is $s$-sparse and symmetric positive-definite, our algorithm has complexity $\widetilde{O}(s\sqrtκ\log(1/ε))$. Technically, our main contribution is the application of the heavy ball momentum method to quantum-inspired classical algorithms for solving linear systems, where we propose two new methods with speedups: quantum-inspired Kaczmarz method with momentum and quantum-inspired coordinate descent method with momentum. Their analysis exploits careful decomposition of the momentum transition matrix and the application of novel spectral norm concentration bounds for independent random matrices. Finally, we also conduct numerical experiments for our algorithms on both synthetic and real-world datasets, and the experimental results support our theoretical claims.

cs.DS↗

arXiv2022

On the Polyak momentum variants of the greedy deterministic single and multiple row-action methods

For solving a consistent system of linear equations, the classical row-action (also known as Kaczmarz) method is a simple while really effective iteration solver. Based on the greedy index selection strategy and Polyak's heavy-ball momentum acceleration technique, we propose two deterministic row-action methods and establish the corresponding convergence theory. We show that our algorithm can linearly converge to a least-squares solution with minimum Euclidean norm. Several numerical studies have been presented to corroborate our theoretical findings. Real-world applications, such as data fitting in computer-aided geometry design, are also presented for illustrative purposes.

math.NA↗

arXiv2022

On the extended randomized multiple row method for solving linear least-squares problems

The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple row method to solve a given overdetermined and inconsistent linear system and analyze its computational complexities at each iteration. We prove that the proposed method can linearly converge in the mean square to the least-squares solution with a minimum Euclidean norm. Several numerical studies are presented to corroborate our theoretical findings. The real-world applications, such as image reconstruction and large noisy data fitting in computer-aided geometric design, are also presented for illustration purposes.

math.NA↗

arXiv2022

Quantum-inspired algorithm for truncated total least squares solution

Total least squares (TLS) methods have been widely used in data fitting. Compared with the least squares method, for TLS problem we takes into account not only the observation errors, but also the errors in the measurement matrix. This is more realistic in practical applications. For the large-scale discrete ill-posed problem $Ax \approx b$, we introduce the quantum-inspired techniques to approximate the truncated total least squares (TTLS) solution. We analyze the accuracy of the quantum-inspired truncated total least squares algorithm and perform numerical experiments to demonstrate the efficiency of our method.

math.NA↗

arXiv2022

A quantum-inspired algorithm for approximating statistical leverage scores

Suppose a matrix $A \in \mathbb{R}^{m \times n}$ of rank $r$ with singular value decomposition $A = U_{A}Σ_{A} V_{A}^{T}$, where $U_{A} \in \mathbb{R}^{m \times r}$, $V_{A} \in \mathbb{R}^{n \times r}$ are orthonormal and $Σ_{A} \in \mathbb{R}^{r \times r}$ is a diagonal matrix. The statistical leverage scores of a matrix $A$ are the squared row-norms defined by $\ell_{i} = \|(U_{A})_{i,:}\|_2^2$, where $i \in [m]$, and the matrix coherence is the largest statistical leverage score. These quantities play an important role in machine learning algorithms such as matrix completion and Nyström-based low rank matrix approximation as well as large-scale statistical data analysis applications, whose usual algorithm complexity is polynomial in the dimension of the matrix $A$. As an alternative to the conventional approach, and inspired by recent development on dequantization techniques, we propose a quantum-inspired algorithm for approximating the statistical leverage scores. We then analyze the accuracy of the algorithm and perform numerical experiments to illustrate the feasibility of our algorithm. Theoretical analysis shows that our novel algorithm takes time polynomial in an integer $k$, condition number $κ$ and logarithm of the matrix size.

math.NA↗

arXiv2022

On the relaxed greedy deterministic row and column iterative methods

For solving the large-scale linear system by iteration methods, we utilize the Petrov-Galerkin conditions and relaxed greedy index selection technique and provide two relaxed greedy deterministic row (RGDR) and column (RGDC) iterative methods, in which one special case of RGDR reduces to the fast deterministic block Kaczmarz method proposed in Chen and Huang (Numer. Algor., 89: 1007-1029, 2021). Our convergence analyses reveal that the resulting algorithms all have the linear convergence rates, which are bounded by the explicit expressions. Numerical examples show that the proposed algorithms are more effective than the relaxed greedy randomized row and column iterative methods.

math.NA↗