arXiv subjects

Jialin Zhang

Publications and source records attributed to Jialin Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2026

SAQNN: Spectral Adaptive Quantum Neural Network as a Universal Approximator

Quantum machine learning (QML), as an interdisciplinary field bridging quantum computing and machine learning, has garnered significant attention in recent years. Currently, the field as a whole faces challenges due to incomplete theoretical foundations for the expressivity of quantum neural networks (QNNs). In this paper we propose a constructive QNN model and demonstrate that it possesses the universal approximation property (UAP), which means it can approximate any square-integrable function up to arbitrary accuracy. Furthermore, it supports switching function bases, thus adaptable to various scenarios in numerical approximation and machine learning. Our model has asymptotic advantages over the best classical feed-forward neural networks in terms of circuit size and achieves optimal parameter complexity when approximating Sobolev functions under $L_2$ norm.

quant-ph↗

arXiv2026

Scalable Multi-QPU Circuit Design for Dicke State Preparation: Optimizing Communication Complexity and Local Circuit Costs

Preparing large-qubit Dicke states is of broad interest in quantum computing and quantum metrology. However, the number of qubits available on a single quantum processing unit (QPU) is limited -- motivating the distributed preparation of such states across multiple QPUs as a practical approach to scalability. In this article, we investigate the distributed preparation of $n$-qubit $k$-excitation Dicke states $D(n,k)$ across a general number $p$ of QPUs, presenting a distributed quantum circuit (each QPU hosting approximately $\lceil n/p \rceil$ qubits) that prepares the state with communication complexity $O(p \log k)$, circuit size $O(nk)$, and circuit depth $O\left(p^2 k + \log k \log (n/k)\right)$. To the best of our knowledge, this is the first construction to simultaneously achieve logarithmic communication complexity and polynomial circuit size and depth. We also establish a lower bound on the communication complexity of $p$-QPU distributed state preparation for a general target state. This lower bound is formulated in terms of the canonical polyadic rank (CP-rank) of a tensor associated with the target state. For the special case $p = 2$, we explicitly compute the CP-rank corresponding to the Dicke state $D(n,k)$ and derive a lower bound of $\lceil\log (k + 1)\rceil$, which shows that the communication complexity of our construction matches this fundamental limit.

quant-ph↗

arXiv2026

On the Fair Allocation to Asymmetric Agents with Binary XOS Valuations

We study the problem of allocating $m$ indivisible goods among $n$ agents, where each agent's valuation is fractionally subadditive (XOS). With respect to AnyPrice Share (APS) fairness, Kulkarni et al. (2024) showed that, when agents have binary marginal values, a $0.1222$-APS allocation can be found in polynomial time, and there exists an instance where no allocation is better than $0.5$-approximate APS. Very recently, Feige and Grinberg (2025) extended the problem to the asymmetric case, where agents may have different entitlements, and improved the approximation ratio to $1/6$ for general XOS valuations. In this work, we focus on the asymmetric setting with binary XOS valuations, and further improve the approximation ratio to $1/2$, which matches the known upper bound. We also present a polynomial-time algorithm to compute such an allocation. Beyond APS fairness, we also study the weighted maximin share (WMMS) fairness. Farhadi et al. (2019) showed that, a $1/n$-WMMS allocation always exists for agents with general additive valuations, and that this approximation ratio is tight. We extend this result to general XOS valuations, where a $1/n$-WMMS allocation still exists, and this approximation ratio cannot be improved even when marginal values are binary. This shows a sharp contrast to binary additive valuations, where an exact WMMS allocation exists and can be found in polynomial time.

cs.GT↗

arXiv2025

A Lyapunov Framework for Quantum Algorithm Design in Combinatorial Optimization with Approximation Ratio Guarantees

In this work, we develop a framework aiming at designing quantum algorithms for combinatorial optimization problems while providing theoretical guarantees on their approximation ratios. The principal innovative aspect of our work is the construction of a time-dependent Lyapunov function that naturally induces a controlled Schrödinger evolution with a time dependent Hamiltonian for maximizing approximation ratios of algorithms. Because the approximation ratio depends on the optimal solution, which is typically elusive and difficult to ascertain a priori, the second novel component is to construct the upper bound of the optimal solution through the current quantum state. By enforcing the non-decreasing property of this Lyapunov function, we not only derive a class of quantum dynamics that can be simulated by quantum devices but also obtain rigorous bounds on the achievable approximation ratio. As a concrete demonstration, we apply our framework to Max-Cut problem, implementing it as an adaptive variational quantum algorithm based on a Hamiltonian ansatz. This algorithm avoids ansatz and graph structural assumptions and bypasses parameter training through a tunable parameter function integrated with measurement feedback.

quant-ph↗

arXiv2025

Diffusion Models at the Drug Discovery Frontier: A Review on Generating Small Molecules versus Therapeutic Peptides

Diffusion models have emerged as a leading framework in generative modeling, poised to transform the traditionally slow and costly process of drug discovery. This review provides a systematic comparison of their application in designing two principal therapeutic modalities: small molecules and therapeutic peptides. We dissect how the unified framework of iterative denoising is adapted to the distinct molecular representations, chemical spaces, and design objectives of each modality. For small molecules, these models excel at structure-based design, generating novel, pocket-fitting ligands with desired physicochemical properties, yet face the critical hurdle of ensuring chemical synthesizability. Conversely, for therapeutic peptides, the focus shifts to generating functional sequences and designing de novo structures, where the primary challenges are achieving biological stability against proteolysis, ensuring proper folding, and minimizing immunogenicity. Despite these distinct challenges, both domains face shared hurdles: the scarcity of high-quality experimental data, the reliance on inaccurate scoring functions for validation, and the crucial need for experimental validation. We conclude that the full potential of diffusion models will be unlocked by bridging these modality-specific gaps and integrating them into automated, closed-loop Design-Build-Test-Learn (DBTL) platforms, thereby shifting the paradigm from mere chemical exploration to the on-demand engineering of novel~therapeutics.

cs.LG↗

arXiv2025

A Unified Complexity-Algorithm Account of Constant-Round QAOA Expectation Computation

The Quantum Approximate Optimization Algorithm (QAOA) is widely studied for combinatorial optimization and has achieved significant advances both in theoretical guarantees and practical performance, yet for general combinatorial optimization problems the expected performance and classical simulability of fixed-round QAOA remain unclear. Focusing on Max-Cut, we first show that for general graphs and any fixed round $p\ge2$, exactly evaluating the expectation of fixed-round QAOA at prescribed angles is $\mathrm{NP}$-hard, and that approximating this expectation within additive error $2^{-O(n)}$ in the number $n$ of vertices is already $\mathrm{NP}$-hard. To evaluate the expected performance of QAOA, we propose a dynamic programming algorithm leveraging tree decomposition. As a byproduct, when the $p$-local treewidth grows at most logarithmically with the number of vertices, this yields a polynomial-time \emph{exact} evaluation algorithm in the graph size $n$. Beyond Max-Cut, we extend the framework to general Binary Unconstrained Combinatorial Optimization (BUCO). Finally, we provide reproducible evaluations for rounds up to $p=3$ on representative structured families, including the generalized Petersen graph $GP(15,2)$, double-layer triangular 2-lifts, and the truncated icosahedron graph $C_{60}$, and report cut ratios while benchmarking against locality-matched classical baselines.

quant-ph↗

arXiv2025

Necessary and Sufficient Conditions for Characterizing Finite Discrete Distributions with Generalized Shannon's Entropy

This article establishes necessary and sufficient conditions under which a finite set of Generalized Shannon's Entropy (GSE) characterizes a finite discrete distribution up to permutation. For an alphabet of cardinality K, it is shown that K-1 distinct positive real orders of GSE are sufficient (and necessary if no multiplicity) to identify the distribution up to permutation. When the distribution has a known multiplicity structure with s distinct values, s-1 orders are sufficient and necessary. These results provide a label-invariant foundation for inference on unordered sample spaces and enable practical goodness-of-fit procedures across disparate alphabets. The findings also suggest new approaches for testing, estimation, and model comparison in settings where moment-based and link-based methods are inadequate.

math.PR↗

arXiv2025

Efficient Non-Adaptive Quantum Algorithms for Tolerant Junta Testing

We consider the problem of deciding whether an $n$-qubit unitary (or $n$-bit Boolean function) is $\varepsilon_1$-close to some $k$-junta or $\varepsilon_2$-far from every $k$-junta, where $k$-junta unitaries act non-trivially on at most $k$ qubits and as the identity on the rest, and $k$-junta Boolean functions depend on at most $k$ variables. For constant numbers $\varepsilon_1,\varepsilon_2$ such that $0 < \varepsilon_1 < \varepsilon_2 < 1$, we show the following. (1) A non-adaptive $O(k\log k)$-query tolerant $(\varepsilon_1,\varepsilon_2)$-tester for $k$-junta unitaries when $2\sqrt{2}\varepsilon_1 < \varepsilon_2$. (2) A non-adaptive tolerant $(\varepsilon_1,\varepsilon_2)$-tester for Boolean functions with $O(k \log k)$ quantum queries when $4\varepsilon_1 < \varepsilon_2$. (3) A $2^{\widetilde{O}(k)}$-query tolerant $(\varepsilon_1,\varepsilon_2)$-tester for $k$-junta unitaries for any $\varepsilon_1,\varepsilon_2$. The first algorithm provides an exponential improvement over the best-known quantum algorithms. The second algorithm shows an exponential quantum advantage over any non-adaptive classical algorithm. The third tester gives the first tolerant junta unitary testing result for an arbitrary gap. Besides, we adapt the first two quantum algorithms to be implemented using only single-qubit operations, thereby enhancing experimental feasibility, with a slightly more stringent requirement for the parameter gap.

quant-ph↗

arXiv2025

Quantum circuit synthesis with SQiSW

The primary objective of quantum circuit synthesis is to efficiently and accurately realize specific quantum algorithms or operations utilizing a predefined set of quantum gates, while also optimizing the circuit size. It holds a pivotal position in Noisy Intermediate-Scale Quantum (NISQ) computation. Historically, most synthesis efforts have predominantly utilized CNOT or CZ gates as the 2-qubit gates. However, the SQiSW gate, also known as the square root of iSWAP gate, has garnered considerable attention due to its outstanding experimental performance with low error rates and high efficiency in 2-qubit gate synthesis. In this paper, we investigate the potential of the SQiSW gate in various synthesis problems by utilizing only the SQiSW gate along with arbitrary single-qubit gates, while optimizing the overall circuit size. For exact synthesis, the upper bound of SQiSW gates to synthesize arbitrary 3-qubit and $n$-qubit gates are 24 and $\frac{139}{192}4^n(1+o(1))$ respectively, which relies on the properties of SQiSW gate in Lie theory and Quantum Shannon Decomposition. We also introduce an exact synthesis scheme for Toffoli gate using only 8 SQiSW gates, which is grounded in numerical observation. More generally, with respect to numerical approximations, we provide a theoretical analysis of a pruning algorithm to reduce the size of the searching space in numerical experiment to $\frac{1}{12}+o(1)$ of previous size, helping us reach the result that 11 SQiSW gates are enough in arbitrary 3-qubit gates synthesis up to an acceptable numerical error.

quant-ph↗

arXiv2025

Mini-Omni-Reasoner: Token-Level Thinking-in-Speaking in Large Speech Models

Reasoning is essential for effective communication and decision-making. While recent advances in LLMs and MLLMs have shown that incorporating explicit reasoning significantly improves understanding and generalization, reasoning in LSMs remains in a nascent stage. Early efforts attempt to transfer the "Thinking-before-Speaking" paradigm from textual models to speech. However, this sequential formulation introduces notable latency, as spoken responses are delayed until reasoning is fully completed, impairing real-time interaction and communication efficiency. To address this, we propose Mini-Omni-Reasoner, a framework that enables reasoning within speech via a novel "Thinking-in-Speaking" formulation. Rather than completing reasoning before producing any verbal output, Mini-Omni-Reasoner interleaves silent reasoning tokens with spoken response tokens at the token level. This design allows continuous speech generation while embedding structured internal reasoning, leveraging the model's high-frequency token processing capability. Although interleaved, local semantic alignment is enforced to ensure that each response token is informed by its preceding reasoning. To support this framework, we introduce Spoken-Math-Problems-3M, a large-scale dataset tailored for interleaved reasoning and response. The dataset ensures that verbal tokens consistently follow relevant reasoning content, enabling accurate and efficient learning of speech-coupled reasoning. Built on a hierarchical Thinker-Talker architecture, Mini-Omni-Reasoner delivers fluent yet logically grounded spoken responses, maintaining both naturalness and precision. On the Spoken-MQA benchmark, it achieves a +19.1% gain in arithmetic reasoning and +6.4% in contextual understanding, with shorter outputs and zero decoding latency.

cs.CL↗

arXiv2025

Quantum Parameter Estimation for Detectors in Constantly Accelerated Motion

We analyze quantum parameter estimation by studying the dynamics of the quantum Fisher information (QFI) for two classes of parameters, acceleration and initial-state weight, in an Unruh-DeWitt detector undergoing four distinct noninertial motions: linear, cusped, catenary, and circular trajectories respectively. We assume that the detector is initialized in a pure superposition state with a weight parameter $θ$ characterizing the probability of the detector occupying each state. Our results reveal that, over long evolution times, the QFI for the acceleration parameter converges to a nonnegative asymptotic value that depends sensitively on the trajectory, whereas the QFI for the weight parameter decays to zero as the system thermalizes. Importantly, for sufficiently large accelerations, one can attain the optimal precision in estimating the acceleration parameter within a finite interaction time, eliminating the need for infinitely long measurements. Comparing trajectories, we find that for small accelerations (relative to the detector's energy gap), linear motion yields the highest QFI for $θ$, while for large accelerations, circular motion becomes optimal for estimating $θ$. By contrast, circular motion offers the best precision for estimating acceleration itself in both the small- and large-acceleration regimes (the latter only at very long times). These contrasting behaviors of QFI across trajectories suggest a novel metrological protocol for inferring the underlying noninertial motion of a quantum probe.

quant-ph↗

arXiv2025

The equilibrium distribution function for strongly nonlinear systems

The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear regimes. We develop a framework to get the equilibrium distributions and dispersion relations in strongly nonlinear many-body systems, incorporating corrections beyond the random phase approximation and capturing intrinsic nonlinear effects. The theory is verified on the nonlinear Schrodinger equation, the Majda-McLaughlin-Tabak model, and the FPUT-beta model, demonstrating its accuracy across distinct types of nonlinear systems. Numerical results show substantial improvements over existing approaches, even in strong nonlinear regimes. This work establishes a theoretical foundation for equilibrium statistical properties in strongly nonlinear systems.

cond-mat.stat-mech↗

arXiv2025

Towards A Robust Group-level Emotion Recognition via Uncertainty-Aware Learning

Group-level emotion recognition (GER) is an inseparable part of human behavior analysis, aiming to recognize an overall emotion in a multi-person scene. However, the existing methods are devoted to combing diverse emotion cues while ignoring the inherent uncertainties under unconstrained environments, such as congestion and occlusion occurring within a group. Additionally, since only group-level labels are available, inconsistent emotion predictions among individuals in one group can confuse the network. In this paper, we propose an uncertainty-aware learning (UAL) method to extract more robust representations for GER. By explicitly modeling the uncertainty of each individual, we utilize stochastic embedding drawn from a Gaussian distribution instead of deterministic point embedding. This representation captures the probabilities of different emotions and generates diverse predictions through this stochasticity during the inference stage. Furthermore, uncertainty-sensitive scores are adaptively assigned as the fusion weights of individuals' face within each group. Moreover, we develop an image enhancement module to enhance the model's robustness against severe noise. The overall three-branch model, encompassing face, object, and scene component, is guided by a proportional-weighted fusion strategy and integrates the proposed uncertainty-aware method to produce the final group-level output. Experimental results demonstrate the effectiveness and generalization ability of our method across three widely used databases.

cs.CV↗

arXiv2025

Noise-Injected Spiking Graph Convolution for Energy-Efficient 3D Point Cloud Denoising

Spiking neural networks (SNNs), inspired by the spiking computation paradigm of the biological neural systems, have exhibited superior energy efficiency in 2D classification tasks over traditional artificial neural networks (ANNs). However, the regression potential of SNNs has not been well explored, especially in 3D point cloud processing. In this paper, we propose noise-injected spiking graph convolutional networks to leverage the full regression potential of SNNs in 3D point cloud denoising. Specifically, we first emulate the noise-injected neuronal dynamics to build noise-injected spiking neurons. On this basis, we design noise-injected spiking graph convolution for promoting disturbance-aware spiking representation learning on 3D points. Starting from the spiking graph convolution, we build two SNN-based denoising networks. One is a purely spiking graph convolutional network, which achieves low accuracy loss compared with some ANN-based alternatives, while resulting in significantly reduced energy consumption on two benchmark datasets, PU-Net and PC-Net. The other is a hybrid architecture that combines ANN-based learning with a high performance-efficiency trade-off in just a few time steps. Our work lights up SNN's potential for 3D point cloud denoising, injecting new perspectives of exploring the deployment on neuromorphic chips while paving the way for developing energy-efficient 3D data acquisition devices.

cs.CV↗

arXiv2024

Entanglement harvesting in cosmic string spacetime

We investigate the entanglement harvesting phenomenon for static detectors that locally interact with massless scalar fields in the cosmic string spacetime, which, though locally flat, features a conical structure defined by a deficit angle. Specifically, we analyze three detector alignments relative to the string: parallel and orthogonal alignments with detectors on the same side of the string, and an orthogonal alignment with detectors on opposite sides of the string. For the alignments on the same side of the string, we observe that the cosmic string's presence can either aid or hinder entanglement harvesting, affecting both the extent of entanglement harvested and the achievable range of interdetector separation. This effect depends on the distance between the detectors and the string and differs markedly from scenarios in a locally flat spacetime with a reflecting boundary, where the boundary invariably extends the harvesting-achievable range. Conversely, for the alignment with detectors on opposite sides of the string, we find that detectors consistently harvest more entanglement than those in a flat spacetime devoid of a cosmic string. This starkly contrasts the behavior observed with detectors on the same side. Interestingly, the presence of a cosmic string expands the harvesting-achievable range for detectors in orthogonal alignment only when near the string, whereas it invariably reduces the achievable range for detectors in parallel alignment.

quant-ph↗

arXiv2024

Boosting Gradient Ascent for Continuous DR-submodular Maximization

Projected Gradient Ascent (PGA) is the most commonly used optimization scheme in machine learning and operations research areas. Nevertheless, numerous studies and examples have shown that the PGA methods may fail to achieve the tight approximation ratio for continuous DR-submodular maximization problems. To address this challenge, we present a boosting technique in this paper, which can efficiently improve the approximation guarantee of the standard PGA to \emph{optimal} with only small modifications on the objective function. The fundamental idea of our boosting technique is to exploit non-oblivious search to derive a novel auxiliary function $F$, whose stationary points are excellent approximations to the global maximum of the original DR-submodular objective $f$. Specifically, when $f$ is monotone and $γ$-weakly DR-submodular, we propose an auxiliary function $F$ whose stationary points can provide a better $(1-e^{-γ})$-approximation than the $(γ^2/(1+γ^2))$-approximation guaranteed by the stationary points of $f$ itself. Similarly, for the non-monotone case, we devise another auxiliary function $F$ whose stationary points can achieve an optimal $\frac{1-\min_{\boldsymbol{x}\in\mathcal{C}}\|\boldsymbol{x}\|_{\infty}}{4}$-approximation guarantee where $\mathcal{C}$ is a convex constraint set. In contrast, the stationary points of the original non-monotone DR-submodular function can be arbitrarily bad~\citep{chen2023continuous}. Furthermore, we demonstrate the scalability of our boosting technique on four problems. In all of these four problems, our resulting variants of boosting PGA algorithm beat the previous standard PGA in several aspects such as approximation ratio and efficiency. Finally, we corroborate our theoretical findings with numerical experiments, which demonstrate the effectiveness of our boosting PGA methods.

cs.LG↗

arXiv2024

Efficient Deterministic Algorithms for Maximizing Symmetric Submodular Functions

Symmetric submodular maximization is an important class of combinatorial optimization problems, including MAX-CUT on graphs and hyper-graphs. The state-of-the-art algorithm for the problem over general constraints has an approximation ratio of $0.432$. The algorithm applies the canonical continuous greedy technique that involves a sampling process. It, therefore, suffers from high query complexity and is inherently randomized. In this paper, we present several efficient deterministic algorithms for maximizing a symmetric submodular function under various constraints. Specifically, for the cardinality constraint, we design a deterministic algorithm that attains a $0.432$ ratio and uses $O(kn)$ queries. Previously, the best deterministic algorithm attains a $0.385-ε$ ratio and uses $O\left(kn (\frac{10}{9ε})^{\frac{20}{9ε}-1}\right)$ queries. For the matroid constraint, we design a deterministic algorithm that attains a $1/3-ε$ ratio and uses $O(kn\log ε^{-1})$ queries. Previously, the best deterministic algorithm can also attain $1/3-ε$ ratio but it uses much larger $O(ε^{-1}n^4)$ queries. For the packing constraints with a large width, we design a deterministic algorithm that attains a $0.432-ε$ ratio and uses $O(n^2)$ queries. To the best of our knowledge, there is no deterministic algorithm for the constraint previously. The last algorithm can be adapted to attain a $0.432$ ratio for single knapsack constraint using $O(n^4)$ queries. Previously, the best deterministic algorithm attains a $0.316-ε$ ratio and uses $\widetilde{O}(n^3)$ queries.

cs.DS↗

arXiv2024

Competitive Auctions with Imperfect Predictions

The competitive auction was first proposed by Goldberg, Hartline, and Wright. In their paper, they introduce the competitive analysis framework of online algorithm designing into the traditional revenue-maximizing auction design problem. While the competitive analysis framework only cares about the worst-case bound, a growing body of work in the online algorithm community studies the learning-augmented framework. In this framework, designers are allowed to leverage imperfect machine-learned predictions of unknown information and pursue better theoretical guarantees when the prediction is accurate(consistency). Meanwhile, designers also need to maintain a nearly-optimal worst-case ratio(robustness). In this work, we revisit the competitive auctions in the learning-augmented setting. We leverage the imperfect predictions of the private value of the bidders and design the learning-augmented mechanisms for several competitive auctions with different constraints, including digital good auctions, limited-supply auctions, and general downward-closed permutation environments. For all these auction environments, our mechanisms enjoy $1$-consistency against the strongest benchmark $OPT$, which is impossible to achieve $O(1)$-competitive without predictions. At the same time, our mechanisms also maintain the $O(1)$-robustness against all benchmarks considered in the traditional competitive analysis. Considering the possible inaccuracy of the predictions, we provide a reduction that transforms our learning-augmented mechanisms into an error-tolerant version, which enables the learning-augmented mechanism to ensure satisfactory revenue in scenarios where the prediction error is moderate.

cs.GT↗