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The local Hamiltonian (LH) problem, the quantum analog of the classical constraint satisfaction problem, is a cornerstone of quantum computation and complexity theory. It is known to be QMA-complete, indicating that it is challenging even for quantum computers. Interestingly, the guided local Hamiltonian (GLH) problem -- an LH problem with a guiding state that has a non-trivial overlap with the ground state -- can be efficiently solved on a quantum computer and is proved to be BQP-complete. This makes the GLH problem a valuable framework for exploring the fundamental separation between classical and quantum computation. Remarkably, the quantum algorithm for solving the GLH problem can be `dequantized' (i.e., made classically simulatable) under certain conditions, such as when only constant accuracy is required and when the Hamiltonian satisfies an unrealistic constant operator norm constraint. In this work, we relieve these restrictions by introducing a dequantized classical algorithm for a randomized quantum imaginary-time evolution quantum algorithm. We demonstrate that it achieves either limited or arbitrary constant accuracy, depending on whether the guiding state's overlap is general or exceeds a certain threshold. Crucially, our approach eliminates the constant operator norm constraint on the Hamiltonian, opening its applicability to realistic problems. Our results advance the classical solution of the GLH problem in practical settings and provide new insights into the boundary between classical and quantum computational power., Comment: 25 pages, 2 figures

Cardiovascular diseases (CVDs) are currently the leading cause of death worldwide, highlighting the critical need for early diagnosis and treatment. Machine learning (ML) methods can help diagnose CVDs early, but their performance relies on access to substantial data with high quality. However, the sensitive nature of healthcare data often restricts individual clinical institutions from sharing data to train sufficiently generalized and unbiased ML models. Federated Learning (FL) is an emerging approach, which offers a promising solution by enabling collaborative model training across multiple participants without compromising the privacy of the individual data owners. However, to the best of our knowledge, there has been limited prior research applying FL to the cardiovascular disease domain. Moreover, existing FL benchmarks and datasets are typically simulated and may fall short of replicating the complexity of natural heterogeneity found in realistic datasets that challenges current FL algorithms. To address these gaps, this paper presents the first real-world FL benchmark for cardiovascular disease detection, named FedCVD. This benchmark comprises two major tasks: electrocardiogram (ECG) classification and echocardiogram (ECHO) segmentation, based on naturally scattered datasets constructed from the CVD data of seven institutions. Our extensive experiments on these datasets reveal that FL faces new challenges with real-world non-IID and long-tail data. The code and datasets of FedCVD are available https://github.com/SMILELab-FL/FedCVD., Comment: 10 pages, 4 figures

This paper develops a comprehensive theoretical framework to analyze the trade-offs between Gross Merchandise Volume (GMV) maximization and social welfare optimization in online food delivery platforms. Using a multi-agent simulation and a dual-model approach based on two-sided market theory and welfare economics, we evaluate the impact of GMV-centric and welfare-centric strategies on platform dynamics, including pricing mechanisms, stakeholder welfare, and market efficiency. Our results show that GMV maximization strategies drive rapid short-term transaction growth but lead to uneven welfare distribution, particularly disadvantaging delivery workers. In contrast, welfare-centric strategies promote a more balanced and equitable distribution of benefits among consumers, restaurants, and delivery workers, enhancing platform sustainability in the long run. These findings provide actionable insights for platform operators and policymakers to design strategies that balance growth with social welfare, ensuring both economic efficiency and fairness.

This paper explores how generative artificial intelligence (AI) affects online platforms where both human creators and AI generate content. We develop a model to understand how generative AI changes supply and demand, impacts traffic distribution, and influences social welfare. Our analysis shows that AI can lead to a huge increase in content supply due to its low cost, which could cause oversupply. While AI boosts content variety, it can also create information overload, lowering user satisfaction and disrupting the market. AI also increases traffic concentration among top creators (the "winner-takes-all" effect) while expanding opportunities for niche content (the "long-tail" effect). We assess how these changes affect consumer and producer benefits, finding that the overall impact depends on the quality of AI-generated content and the level of information overload. Through simulation experiments, we test policy ideas, such as adjusting platform fees and recommendations, to reduce negative effects and improve social welfare. The results highlight the need for careful management of AI's role in online content platforms to maintain a healthy balance

This paper develops a theoretical framework to analyze live streaming platforms as two-sided markets connecting streamers and viewers, focusing on the "head effect" where a few top streamers attract most viewers due to strong network effects and platform policies like commission rates and traffic allocation algorithms. Using static and dynamic models, it examines how these factors lead to traffic concentration and winner-takes-all scenarios. The welfare implications are assessed, revealing that while such concentration may enhance consumer utility short-term, it can reduce content diversity and overall social welfare in the long run. The paper proposes policy interventions to adjust traffic allocation, promoting a more equitable distribution of viewers across streamers, and demonstrates through simulations that combining multiple policies can significantly reduce market concentration and enhance social welfare

Efficient classical simulation of the Schrodinger equation is central to quantum mechanics, as it is crucial for exploring complex natural phenomena and understanding the fundamental distinctions between classical and quantum computation. Although simulating general quantum dynamics is BQP-complete, tensor networks allow efficient simulation of short-time evolution in 1D systems. However, extending these methods to higher dimensions becomes significantly challenging when the area law is violated. In this work, we tackle this challenge by introducing an efficient classical algorithm for simulating short-time dynamics in 2D quantum systems, utilizing cluster expansion and shallow quantum circuit simulation. Our algorithm has wide-ranging applications, including an efficient dequantization method for estimating quantum eigenvalues and eigenstates, simulating superconducting quantum computers, dequantizing quantum variational algorithms, and simulating constant-gap adiabatic quantum evolution. Our results reveal the inherent simplicity in the complexity of short-time 2D quantum dynamics and highlight the limitations of noisy intermediate-scale quantum hardware, particularly those confined to 2D topological structures. This work advances our understanding of the boundary between classical and quantum computation and the criteria for achieving quantum advantage., Comment: Revise some typos in the previous version

This paper presents a novel unified theoretical framework for understanding Transformer architectures by integrating Partial Differential Equations (PDEs), Neural Information Flow Theory, and Information Bottleneck Theory. We model Transformer information dynamics as a continuous PDE process, encompassing diffusion, self-attention, and nonlinear residual components. Our comprehensive experiments across image and text modalities demonstrate that the PDE model effectively captures key aspects of Transformer behavior, achieving high similarity (cosine similarity > 0.98) with Transformer attention distributions across all layers. While the model excels in replicating general information flow patterns, it shows limitations in fully capturing complex, non-linear transformations. This work provides crucial theoretical insights into Transformer mechanisms, offering a foundation for future optimizations in deep learning architectural design. We discuss the implications of our findings, potential applications in model interpretability and efficiency, and outline directions for enhancing PDE models to better mimic the intricate behaviors observed in Transformers, paving the way for more transparent and optimized AI systems.

This paper explores the application of Stochastic Differential Equations (SDE) to interpret the text generation process of Large Language Models (LLMs) such as GPT-4. Text generation in LLMs is modeled as a stochastic process where each step depends on previously generated content and model parameters, sampling the next word from a vocabulary distribution. We represent this generation process using SDE to capture both deterministic trends and stochastic perturbations. The drift term describes the deterministic trends in the generation process, while the diffusion term captures the stochastic variations. We fit these functions using neural networks and validate the model on real-world text corpora. Through numerical simulations and comprehensive analyses, including drift and diffusion analysis, stochastic process property evaluation, and phase space exploration, we provide deep insights into the dynamics of text generation. This approach not only enhances the understanding of the inner workings of LLMs but also offers a novel mathematical perspective on language generation, which is crucial for diagnosing, optimizing, and controlling the quality of generated text.

To improve the quality of experience (QoE) in video communication over lossy networks, this paper presents a transmission method that jointly optimizes buffer delay and Hybrid Automatic Repeat request (HARQ), referred to as BD-HARQ. This method operates on packet group and employs dynamic buffer delay combined with HARQ strategy for transmission. By defining the QoE based on metrics such as buffer delay, Forward Error Correction (FEC) redundancy, and data recovery rate, the proposed method derives its closed-form expression through rigorous mathematical modeling and analysis. The optimal transmission parameters, i.e., the buffer delay and the FEC redundancy, are then determined and implemented, guaranteeing the real-time performance, transmission efficiency, and data recovery rate of video communication. Experimental results demonstrate that the proposed method aligns well with its theoretical expectations, and that it can provide up to 13.7% higher QoE compared to existing methods and increase the tolerance for packet loss rate from 15%-22% to up to 31% while maintaining a high QoE., Comment: 6 pages, 5figures

This study presents a novel approach that leverages Neural Ordinary Differential Equations (Neural ODEs) to unravel the intricate relationships between inputs and outputs in Large Language Models (LLMs), and employs robust control to fine-tune outputs to meet predefined standards. Central to our methodology is the transformation of LLM inputs and outputs into a lower-dimensional latent space, facilitating a detailed examination of the information processing pathways within LLMs. Neural ODEs play a pivotal role in this investigation by providing a dynamic model that captures the continuous evolution of data within the LLMs. Additionally, robust control mechanisms are applied to strategically adjust the model's outputs, ensuring they not only maintain high quality and reliability but also adhere to specific performance criteria. This fusion of Neural ODEs and robust control represents a significant advancement in LLM interpretability, offering a comprehensive framework that elucidates the previously opaque mechanisms of these complex models. Our empirical results validate the effectiveness of this integrated approach, making a substantial contribution to the field of explainable AI by merging advanced machine learning techniques with the critical need for transparency and control in AI outputs.

While non-Hermitian physics has attracted considerable attention, current studies are limited to small or classically solvable systems. Quantum computing, as a powerful eigensolver, have predominantly been applied to Hermitian domain, leaving their potential for studying non-Hermitian problems largely unexplored. We extend the power of quantum computing to general non-Hermitian eigenproblems. Our approach works for finding eigenvalues without extra constrains, or eigenvalues closest to specified points or lines, thus extending results for ground energy and energy gap problems for Hermitian matrices. Our algorithms have broad applications, and as examples, we consider two central problems in non-Hermitian physics. Firstly, our approach is the first to offer an efficient quantum solution to the witness of spontaneous $PT$-symmetry breaking, and provide provable, exponential quantum advantage. Secondly, our approach enables the estimation of Liouvillian gap, which is crucial for characterizing relaxation times. Our general approach can also find applications in many other areas, such as the study of Markovian stochastic processes. These results underscore the significance of our quantum algorithms for addressing practical eigenproblems across various disciplines., Comment: 7+30 pages, 2+6 figures

The language evaluation information of the interactive group decision method at present is based on the one-dimension language variable. At the same time, multi-attribute group decision making method based on two-dimension linguistic information only use single-stage and static evaluation method. In this paper, we propose a dynamic group decision making method based on two-dimension linguistic information, combining dynamic interactive group decision making methods with two-dimensional language evaluation information The method first use Two-Dimensional Uncertain Linguistic Generalized Weighted Aggregation (DULGWA) Operators to aggregate the preference information of each decision maker, then adopting dynamic information entropy method to obtain weights of attributes at each stage. Finally we propose the group consistency index to quantify the termination conditions of group interaction. One example is given to verify the developed approach and to demonstrate its effectiveness, Comment: arXiv admin note: substantial text overlap with arXiv:2311.18116

Noise is in general inevitable and detrimental to practical and useful quantum communication and computation. Under the resource theory framework, resource distillation serves as a generic tool to overcome the effect of noise. Yet, conventional resource distillation protocols generally require operations on multi-copies of resource states, and strong limitations exist that restrict their practical utilities. Recently, by relaxing the setting of resource distillation to only approximating the measurement statistics instead of the quantum state, a resource-frugal protocol, virtual resource distillation, is proposed, which allows more effective distillation of noisy resources. Here, we report its experimental implementation on a photonic quantum system for the distillation of quantum coherence (up to dimension 4) and bipartite entanglement. We show the virtual distillation of the maximal superposed state of dimension four from the state of dimension two, an impossible task in conventional coherence distillation. Furthermore, we demonstrate the virtual distillation of entanglement with operations acting only on a single copy of the noisy EPR pair and showcase the quantum teleportation task using the virtually distilled EPR pair with a significantly improved fidelity of the teleported state. These results illustrate the feasibility of the virtual resource distillation method and pave the way for accurate manipulation of quantum resources with noisy quantum hardware., Comment: 15 pages, 8 figures

Near-term quantum devices generally suffer from shallow circuit depth and hence limited expressivity due to noise and decoherence. To address this, we propose tensor network assisted parameterized quantum circuits, which concatenate a classical tensor network operator with a quantum circuit to effectively increase the circuit's expressivity without requiring a physically deeper circuit. We present a framework for tensor network-assisted variational quantum algorithms that can solve quantum many-body problems using shallower quantum circuits. We demonstrate the efficiency of this approach by considering two examples of unitary matrix product operators and unitary tree tensor networks, showing that they can both be implemented efficiently. Through numerical simulations, we show that the expressivity of these circuits is greatly enhanced with the assistance of tensor networks. We apply our method to 2D Ising models and 1D time crystal Hamiltonian models with up to 16 qubits, and demonstrate that our approach consistently outperforms conventional methods using shallow quantum circuits., Comment: 9 pages, 4 figures, 41 references

Quantum computational chemistry has emerged as an important application of quantum computing. Hybrid quantum-classical computing methods, such as variational quantum eigensolvers (VQE), have been designed as promising solutions to quantum chemistry problems, yet challenges due to theoretical complexity and experimental imperfections hinder progress in achieving reliable and accurate results. Experimental works for solving electronic structures are consequently still restricted to nonscalable (hardware efficient) or classically simulable (Hartree-Fock) ansatz, or limited to a few qubits with large errors. The experimental realisation of scalable and high-precision quantum chemistry simulation remains elusive. Here, we address the critical challenges {associated with} solving molecular electronic structures using noisy quantum processors. Our protocol presents significant improvements in the circuit depth and running time, key metrics for chemistry simulation. Through systematic hardware enhancements and the integration of error mitigation techniques, we push forward the limit of experimental quantum computational chemistry and successfully scale up the implementation of VQE with an optimised unitary coupled-cluster ansatz to 12 qubits. We produce high-precision results of the ground-state energy for molecules with error suppression by around two orders of magnitude. We achieve chemical accuracy for H$_2$ at all bond distances and LiH at small bond distances in the experiment, even beyond the two recent concurrent works. Our work demonstrates a feasible path towards a scalable solution to electronic structure calculation, validating the key technological features and identifying future challenges for this goal., Comment: 11 pages, 4 figures in the main text, and 29 pages supplementary materials with 17 figures

Quantum computing and quantum Monte Carlo (QMC) are respectively the state-of-the-art quantum and classical computing methods for understanding many-body quantum systems. Here, we propose a hybrid quantum-classical algorithm that integrates these two methods, inheriting their distinct features in efficient representation and manipulation of quantum states and overcoming their limitations. We first introduce non-stoquasticity indicators (NSIs) and their upper bounds, which measure the sign problem, the most notable limitation of QMC. We show that our algorithm could greatly mitigate the sign problem, which decreases NSIs with the assistance of quantum computing. Meanwhile, the use of quantum Monte Carlo also increases the expressivity of shallow quantum circuits, allowing more accurate computation that is conventionally achievable only with much deeper circuits. We numerically test and verify the method for the N$_2$ molecule (12 qubits) and the Hubbard model (16 qubits). Our work paves the way to solving practical problems with intermediate-scale and early-fault tolerant quantum computers, with potential applications in chemistry, condensed matter physics, materials, high energy physics, etc.