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Quantum state tomography (QST) via local measurements on reduced density matrices (LQST) is a promising approach but becomes impractical for large systems. To tackle this challenge, we developed an efficient quantum state tomography method inspired by quantum overlapping tomography [Phys. Rev. Lett. 124, 100401(2020)], which utilizes parallel measurements (PQST). In contrast to LQST, PQST significantly reduces the number of measurements and offers more robustness against shot noise. Experimentally, we demonstrate the feasibility of PQST in a tree-like superconducting qubit chip by designing high-efficiency circuits, preparing W states, ground states of Hamiltonians and random states, and then reconstructing these density matrices using full quantum state tomography (FQST), LQST, and PQST. Our results show that PQST reduces measurement cost, achieving fidelities of 98.68\% and 95.07\% after measuring 75 and 99 observables for 6-qubit and 9-qubit W states, respectively. Furthermore, the reconstruction of the largest density matrix of the 12-qubit W state is achieved with the similarity of 89.23\% after just measuring $243$ parallel observables, while $3^{12}=531441$ complete observables are needed for FQST. Consequently, PQST will be a useful tool for future tasks such as the reconstruction, characterization, benchmarking, and properties learning of states., Comment: To appear in PRL(2024)

Visual-inertial systems have been widely studied and applied in the last two decades, mainly due to their low cost and power consumption, small footprint, and high availability. Such a trend simultaneously leads to a large amount of visual-inertial calibration methods being presented, as accurate spatiotemporal parameters between sensors are a prerequisite for visual-inertial fusion. In our previous work, i.e., iKalibr, a continuous-time-based visual-inertial calibration method was proposed as a part of one-shot multi-sensor resilient spatiotemporal calibration. While requiring no artificial target brings considerable convenience, computationally expensive pose estimation is demanded in initialization and batch optimization, limiting its availability. Fortunately, this could be vastly improved for the RGBDs with additional depth information, by employing mapping-free ego-velocity estimation instead of mapping-based pose estimation. In this paper, we present the continuous-time ego-velocity estimation-based RGBD-inertial spatiotemporal calibration, termed as iKalibr-RGBD, which is also targetless but computationally efficient. The general pipeline of iKalibr-RGBD is inherited from iKalibr, composed of a rigorous initialization procedure and several continuous-time batch optimizations. The implementation of iKalibr-RGBD is open-sourced at (https://github.com/Unsigned-Long/iKalibr) to benefit the research community.

The two-dimensional (2D) Cu(CrSe$_2$)$_2$ monolayer stands out for its combined ferromagnetic (FM), ferroelectric (FE), and metallic properties, marking itself as a prominent 2D multiferroic metal. This work studies those properties and the relevant physics, using density functional calculations, Monte Carlo simulations, and $ab$ $initio$ molecular dynamics. Our results show that Cu(CrSe$_2$)$_2$ monolayer is in the Cr$^{3+}$ $t_{2g}^3$ state with $S$ = 3/2 and Cu$^{1+}$ $3d^{10}$ with $S$ = 0. A ligand hole in the Se 4$p$ orbitals gives rise to metallic behavior and enhances the FM coupling between the local Cr$^{3+}$ $S$ = 3/2 spins. The observed in-plane magnetic anisotropy primarily arises from exchange anisotropy, which is associated with the Cr-Se-Cr itinerant ferromagnetism. In contrast, both single-ion anisotropy and shape magnetic anisotropy contribute negligibly. The Dzyaloshinskii-Moriya interaction is also quite weak, only about 3\% of the intralayer exchange parameters. Our Monte Carlo simulations show a FM Curie temperature ($T_{\rm C}$) of 190 K. Moreover, the monolayer exhibits a vertical FE polarization of 1.79 pC/m and a FE polarization switching barrier of 182 meV/f.u., and the FE state remains stable above 800 K as shown by $ab$ $initio$ molecular dynamics simulations. Furthermore, a magnetoelectric coupling is partially manifested by a magnetization rotation from in-plane to out-of-plane associated with a FE-to-paraelectric transition. The magnetization rotation can also be induced by either hole or electron doping, and the hole doping increases the $T_{\rm C}$ up to 238 K. In addition, tensile strain reduces the FE polarization but enhances $T_{\rm C}$ to 290 K, while a compressive strain gives an opposite effect. Therefore, the multiferroic metallic Cu(CrSe$_2$)$_2$ monolayer may be explored for advanced multifunctional electronic devices., Comment: 14 pages, 7 figures

Sampling-based decoding strategies have been widely adopted for Large Language Models (LLMs) in numerous applications, which target a balance between diversity and quality via temperature tuning and tail truncation (e.g., top-k and top-p sampling). Considering the high dynamic range of the candidate next-token given different prefixes, recent studies propose to adaptively truncate the tail of LLM's predicted distribution. Although improved results haven been reported with these methods on open-ended text generation tasks, the results are highly dependent on the curated truncation parameters and exemplar text. In this paper, we propose a systematic way to estimate the intrinsic capacity of a truncation sampling method by considering the trade-off between diversity and risk at each decoding step, based on our collected prefix tree which preserves the context of a full sentence. Our work provides a comprehensive comparison between existing truncation sampling methods, as well as their recommended parameters as a guideline for users.

Mixers play a crucial role in superconducting quantum computing, primarily by facilitating frequency conversion of signals to enable precise control and readout of quantum states. However, imperfections, particularly carrier leakage and unwanted sideband signal, can significantly compromise control fidelity. To mitigate these defects, regular and precise mixer calibrations are indispensable, yet they pose a formidable challenge in large-scale quantum control. Here, we introduce an in situ calibration technique and outcome-focused mixer calibration scheme using superconducting qubits. Our method leverages the qubit's response to imperfect signals, allowing for calibration without modifying the wiring configuration. We experimentally validate the efficacy of this technique by benchmarking single-qubit gate fidelity and qubit coherence time., Comment: 9 pages, 7 figures

Aided inertial navigation system (INS), typically consisting of an inertial measurement unit (IMU) and an exteroceptive sensor, has been widely accepted as a feasible solution for navigation. Compared with vision-aided and LiDAR-aided INS, radar-aided INS could achieve better performance in adverse weather conditions since the radar utilizes low-frequency measuring signals with less attenuation effect in atmospheric gases and rain. For such a radar-aided INS, accurate spatiotemporal transformation is a fundamental prerequisite to achieving optimal information fusion. In this work, we present RIs-Calib: a spatiotemporal calibrator for multiple 3D radars and IMUs based on continuous-time estimation, which enables accurate spatiotemporal calibration and does not require any additional artificial infrastructure or prior knowledge. Our approach starts with a rigorous and robust procedure for state initialization, followed by batch optimizations, where all parameters can be refined to global optimal states steadily. We validate and evaluate RIs-Calib on both simulated and real-world experiments, and the results demonstrate that RIs-Calib is capable of accurate and consistent calibration. We open-source our implementations at (https://github.com/Unsigned-Long/RIs-Calib) to benefit the research community.

This study investigates the spin-orbital states of FePS3 and FePSe3 monolayers and the origin of their Ising zigzag AFM, using DFT, crystal field level diagrams, superexchange analyses, and parallel tempering MC simulations. Our calculations show that under the trigonal elongation of the FeS6 (FeSe6) octahedra, the $e_g^\pi$ doublet of the Fe 3d crystal field levels lies lower than the $a_{1g}$ singlet by about 108 meV (123 meV), which is much larger than the strength of Fe 3d SOC. Then, the half-filled minority-spin $e_g^\pi$ doublet of the high-spin Fe$^{2+}$ ions ($d^{5\uparrow,1\downarrow}$) splits by the SOC into the lower $L_{z+}$ and higher $L_{z-}$ states. The spin-orbital ground state $d^{5\uparrow}$$L_{z+}^{1\downarrow}$ formally with $S_z$ = 2 and $L_z$ = 1 gives the large z-axis spin/orbital moments of 3.51/0.76 $\mu_{B}$ (3.41/0.67 $\mu_{B}$) for FePS$_3$ (FePSe$_3$) monolayer, and both the moments are reduced by the strong (stronger) Fe 3d hybridizations with S 3p (Se 4p) states. As a result, FePS3 (FePSe3) monolayer has a huge perpendicular single-ion anisotropy energy of 19.4 meV (14.9 meV), giving an Ising-type magnetism. Moreover, via the maximally localized Wannier functions, we find that the first nearest neighboring (1NN) Fe-Fe pair has large hopping parameters in between some specific orbitals, and so does the 3NN Fe-Fe pair. In contrast, the 2NN Fe-Fe pair has much smaller hopping parameters and the 4NN Fe-Fe pair has negligibly small ones. Then, a combination of those hopping parameters and the superexchange picture can readily explain the computed strong 1NN ferromagnetic coupling and the strong 3NN antiferromagnetic one but the relatively much smaller 2NN antiferromagnetic coupling. Furthermore, our PTMC simulations give TN of 119 K for FePS3 monolayer and also predict for FePSe3 monolayer the same magnetic structure with a close or even higher TN., Comment: 14 pages, 9 figures, 3 tables

Generation and preservation of quantum entanglement are among the primary tasks in quantum information processing. State stabilization via quantum bath engineering offers a resource-efficient approach to achieve this objective. However, current methods for engineering dissipative channels to stabilize target entangled states often require specialized hardware designs, complicating experimental realization and hindering their compatibility with scalable quantum computation architectures. In this work, we propose and experimentally demonstrate a stabilization protocol readily implementable in the mainstream integrated superconducting quantum circuits. The approach utilizes a Raman process involving a resonant (or nearly resonant) superconducting qubit array and their dedicated readout resonators to effectively emerge nonlocal dissipative channels. Leveraging individual controllability of the qubits and resonators, the protocol stabilizes two-qubit Bell states with a fidelity of $90.7\%$, marking the highest reported value in solid-state platforms to date. Furthermore, by extending this strategy to include three qubits, an entangled $W$ state is achieved with a fidelity of $86.2\%$, which has not been experimentally investigated before. Notably, the protocol is of practical interest since it only utilizes existing hardware common to standard operations in the underlying superconducting circuits, thereby facilitating the exploration of many-body quantum entanglement with dissipative resources.

The integrated inertial system, typically integrating an IMU and an exteroceptive sensor such as radar, LiDAR, and camera, has been widely accepted and applied in modern robotic applications for ego-motion estimation, motion control, or autonomous exploration. To improve system accuracy, robustness, and further usability, both multiple and various sensors are generally resiliently integrated, which benefits the system performance regarding failure tolerance, perception capability, and environment compatibility. For such systems, accurate and consistent spatiotemporal calibration is required to maintain a unique spatiotemporal framework for multi-sensor fusion. Considering most existing calibration methods (i) are generally oriented to specific integrated inertial systems, (ii) often only focus on spatial determination, (iii) usually require artificial targets, lacking convenience and usability, we propose iKalibr: a unified targetless spatiotemporal calibration framework for resilient integrated inertial systems, which overcomes the above issues, and enables both accurate and consistent calibration. Altogether four commonly employed sensors are supported in iKalibr currently, namely IMU, radar, LiDAR, and camera. The proposed method starts with a rigorous and efficient dynamic initialization, where all parameters in the estimator would be accurately recovered. Following that, several continuous-time-based batch optimizations would be carried out to refine initialized parameters to global optimal ones. Sufficient real-world experiments were conducted to verify the feasibility and evaluate the calibration performance of iKalibr. The results demonstrate that iKalibr can achieve accurate resilient spatiotemporal calibration. We open-source our implementations at (https://github.com/Unsigned-Long/iKalibr) to benefit the research community.

In this paper, we investigate the validity of a quantitative version of stability for the critical Hardy-H\'enon equation \begin{equation*} H(u):=\div(|x|^{-2a}\nabla u)+|x|^{-pb}|u|^{p-2}u=0,\quad u\in D_a^{1,2}(\R^n), \end{equation*} \begin{equation*} n\geq 2,\quad a

Vision-and-Language Navigation (VLN) aims to develop embodied agents that navigate based on human instructions. However, current VLN frameworks often rely on static environments and optimal expert supervision, limiting their real-world applicability. To address this, we introduce Human-Aware Vision-and-Language Navigation (HA-VLN), extending traditional VLN by incorporating dynamic human activities and relaxing key assumptions. We propose the Human-Aware 3D (HA3D) simulator, which combines dynamic human activities with the Matterport3D dataset, and the Human-Aware Room-to-Room (HA-R2R) dataset, extending R2R with human activity descriptions. To tackle HA-VLN challenges, we present the Expert-Supervised Cross-Modal (VLN-CM) and Non-Expert-Supervised Decision Transformer (VLN-DT) agents, utilizing cross-modal fusion and diverse training strategies for effective navigation in dynamic human environments. A comprehensive evaluation, including metrics considering human activities, and systematic analysis of HA-VLN's unique challenges, underscores the need for further research to enhance HA-VLN agents' real-world robustness and adaptability. Ultimately, this work provides benchmarks and insights for future research on embodied AI and Sim2Real transfer, paving the way for more realistic and applicable VLN systems in human-populated environments., Comment: 30 pages, 18 figures, Project Page: https://lpercc.github.io/HA3D_simulator/

Random fluctuations can lead to cooperative effects in complex systems. We here report the experimental observation of noise-induced quantum synchronization in a chain of superconducting transmon qubits with nearest-neighbor interactions. The application of Gaussian white noise to a single site leads to synchronous oscillations in the entire chain. We show that the two synchronized end qubits are entangled, with nonzero concurrence, and that they belong to a class of generalized Bell states known as maximally entangled mixed states, whose entanglement cannot be increased by any global unitary. We further demonstrate the stability against frequency detuning of both synchronization and entanglement by determining the corresponding generalized Arnold tongue diagrams. Our results highlight the constructive influence of noise in a quantum many-body system and uncover the potential role of synchronization for mixed-state quantum information science.

We design 3D-printed motor-driven active particles and find that their dynamics can be characterized using the model of overdamped chiral active Brownian particles (ABPs), as demonstrated by measured angular statistics and translational mean squared displacements (MSDs). Furthermore, we propose a minimal model that reproduces the double-peak velocity distributions and further predicts a transition from the single-peak to the double-peak displacement distributions in short-time regimes. The model provides a clear physics picture of these phenomena, originating from the competition between the active motion and the translational diffusion. Our experiments confirm such picture. The minimal model enhances our understanding of activity-driven non-Gaussian phenomena. The designed particles could be further applied in the study of collective chiral motions.

Large language models (LLMs) have excelled across domains, also delivering notable performance on the medical evaluation benchmarks, such as MedQA. However, there still exists a significant gap between the reported performance and the practical effectiveness in real-world medical scenarios. In this paper, we aim to explore the causes of this gap by employing a multifaceted examination schema to systematically probe the actual mastery of medical knowledge by current LLMs. Specifically, we develop a novel evaluation framework MultifacetEval to examine the degree and coverage of LLMs in encoding and mastering medical knowledge at multiple facets (comparison, rectification, discrimination, and verification) concurrently. Based on the MultifacetEval framework, we construct two multifaceted evaluation datasets: MultiDiseK (by producing questions from a clinical disease knowledge base) and MultiMedQA (by rephrasing each question from a medical benchmark MedQA into multifaceted questions). The experimental results on these multifaceted datasets demonstrate that the extent of current LLMs in mastering medical knowledge is far below their performance on existing medical benchmarks, suggesting that they lack depth, precision, and comprehensiveness in mastering medical knowledge. Consequently, current LLMs are not yet ready for application in real-world medical tasks. The codes and datasets are available at https://github.com/THUMLP/MultifacetEval., Comment: Accepted by IJCAI 2024

SoftMax is a ubiquitous ingredient of modern machine learning algorithms. It maps an input vector onto a probability simplex and reweights the input by concentrating the probability mass at large entries. Yet, as a smooth approximation to the Argmax function, a significant amount of probability mass is distributed to other, residual entries, leading to poor interpretability and noise. Although sparsity can be achieved by a family of SoftMax variants, they often require an alternative loss function and do not preserve multi-modality. We show that this trade-off between multi-modality and sparsity limits the expressivity of SoftMax as well as its variants. We provide a solution to this tension between objectives by proposing a piece-wise differentiable function, termed MultiMax, which adaptively modulates the output distribution according to input entry range. Through comprehensive analysis and evaluation, we show that MultiMax successfully produces a distribution that supresses irrelevant entries while preserving multimodality, with benefits in image classification, language modeling and machine translation. The code is available at https://github.com/ZhouYuxuanYX/MultiMax., Comment: Accepted at ICML 2024

Superconducting qubits are a promising platform for building fault-tolerant quantum computers, with recent achievement showing the suppression of logical error with increasing code size. However, leakage into non-computational states, a common issue in practical quantum systems including superconducting circuits, introduces correlated errors that undermine QEC scalability. Here, we propose and demonstrate a leakage reduction scheme utilizing tunable couplers, a widely adopted ingredient in large-scale superconducting quantum processors. Leveraging the strong frequency tunability of the couplers and stray interaction between the couplers and readout resonators, we eliminate state leakage on the couplers, thus suppressing space-correlated errors caused by population propagation among the couplers. Assisted by the couplers, we further reduce leakage to higher qubit levels with high efficiency (98.1%) and low error rate on the computational subspace (0.58%), suppressing time-correlated errors during QEC cycles. The performance of our scheme demonstrates its potential as an indispensable building block for scalable QEC with superconducting qubits., Comment: 25 pages, 15 figures

Visual simultaneous localization and mapping (VSLAM) has broad applications, with state-of-the-art methods leveraging deep neural networks for better robustness and applicability. However, there is a lack of research in fusing these learning-based methods with multi-sensor information, which could be indispensable to push related applications to large-scale and complex scenarios. In this paper, we tightly integrate the trainable deep dense bundle adjustment (DBA) with multi-sensor information through a factor graph. In the framework, recurrent optical flow and DBA are performed among sequential images. The Hessian information derived from DBA is fed into a generic factor graph for multi-sensor fusion, which employs a sliding window and supports probabilistic marginalization. A pipeline for visual-inertial integration is firstly developed, which provides the minimum ability of metric-scale localization and mapping. Furthermore, other sensors (e.g., global navigation satellite system) are integrated for driftless and geo-referencing functionality. Extensive tests are conducted on both public datasets and self-collected datasets. The results validate the superior localization performance of our approach, which enables real-time dense mapping in large-scale environments. The code has been made open-source (https://github.com/GREAT-WHU/DBA-Fusion).

Two-dimensional van der Waals magnetic materials are of great current interest for their promising applications in spintronics. In this work, using density functional theory calculations in combination with the maximally localized Wannier functions method and the magnetic anisotropy analyses, we study the electronic and magnetic properties of MnPSe$_3$ monolayer. Our results show that it is a charge transfer antiferromagnetic (AF) insulator. For this Mn$^{2+}$ $3d^5$ system, although it seems straightforward to explain the AF ground state using the direct exchange, we find that the near 90$^\circ$ Mn-Se-Mn charge transfer type superexchange plays a dominant role in stabilizing the AF ground state. Moreover, our results indicate that although the shape anisotropy favors an out-of-plane spin orientation, the spin-orbit coupling (SOC) leads to the experimentally observed in-plane spin orientation. We prove that the actual dominant contribution to the magnetic anisotropy comes from the second-order perturbation of the SOC, by analyzing its distribution over the reciprocal space. Using the AF exchange and anisotropy parameters obtained from our calculations, our Monte Carlo simulations give the N\'eel temperature $T_{\rm N}=47$ K for MnPSe$_3$ monolayer, which agrees with the experimental 40 K. Furthermore, our calculations show that under a uniaxial tensile (compressive) strain, N\'eel vector would be parallel (perpendicular) to the strain direction, which well reproduces the recent experiments. We also predict that $T_{\rm N}$ would be increased by a compressive strain., Comment: 8 pages, 9 figures

DEX, or decentralized exchange, is a prominent class of decentralized finance (DeFi) applications on blockchains, attracting a total locked value worth tens of billions of USD today. This paper presents the first large-scale empirical study that uncovers unfair trades on popular DEX services on Ethereum and Binance Smart Chain (BSC). By joining and analyzing 60 million transactions, we find 671,400 unfair trades on all six measured DEXes, including Uniswap, Balancer, and Curve. Out of these unfair trades, we attribute 55,000 instances, with high confidence, to token thefts that cause a value loss of more than 3.88 million USD. Furthermore, the measurement study uncovers previously unknown causes of extractable value and real-world adaptive strategies to these causes. Finally, we propose countermeasures to redesign secure DEX protocols and to harden deployed services against the discovered security risks.

Two-dimensional (2D) magnetic materials are of current great interest for their promising applications in spintronics. Strong magnetic coupling and anisotropy are both highly desirable for the achievement of a high temperature magnetic order. Here we propose the unusual high valent FeS$_2$ hexagonal monolayer as such a candidate for a strong Ising 2D ferromagnet (FM), by spin-orbital state analyses, first-principles calculations, and the renormalized spin-wave theory (RSWT). We find that very importantly, the high valent Fe$^{4+}$ ion is in the low-spin state ($t_{2g}^{4}$, $S$=1) with degenerate $t_{2g}$ orbitals rather than the high-spin state ($t_{2g}^{3}e_g^{1}$, $S$=2). It is the low-spin state that allows to carry a large perpendicular orbital moment and then produces a huge single ion anisotropy (SIA) of 25 meV/Fe. Moreover, the negative charge transfer character associated with the unusual high valence, strong Fe $3d$-S $3p$ hybridization, wide bands, and a small band gap all help to establish a strong superexchange. Indeed, our first-principles calculations confirm the strong FM superexchange and the huge perpendicular SIA, both of which are further enhanced by a compressive strain. Then, our RSWT calculations predict that the FM $T_{\rm C}$ is 261 K for the pristine FeS$_2$ monolayer and could be increased to 409 K under the compressive --5\% strain. The high $T_{\rm C}$ is also reproduced by our Monte Carlo (MC) simulations. Therefore, it is worth exploring the high-$T_{\rm C}$ Ising FMs in the high valent 2D magnetic materials with degenerate orbitals., Comment: 13 pages, 5 figures

As quantum circuits become more integrated and complex, additional error sources that were previously insignificant start to emerge. Consequently, the fidelity of quantum gates benchmarked under pristine conditions falls short of predicting their performance in realistic circuits. To overcome this problem, we must improve their robustness against pertinent error models besides isolated fidelity. Here we report the experimental realization of robust quantum gates in superconducting quantum circuits based on a geometric framework for diagnosing and correcting various gate errors. Using quantum process tomography and randomized benchmarking, we demonstrate robust single-qubit gates against quasi-static noise and spatially-correlated noise in a broad range of strengths, which are common sources of coherent errors in large-scale quantum circuit. We also apply our method to non-static noises and to realize robust two-qubit gates. Our work provides a versatile toolbox for achieving noise-resilient complex quantum circuits., Comment: 6 pages, 4 figures plus Supplementary Information

In this paper, we investigate the following Caffarelli-Kohn-Nirenberg inequality: \begin{equation*} \left(\int_{\mathbb{R}^n}|x|^{-pa}|\nabla u|^pdx\right)^{\frac{1}{p}}\geq S(p,a,b)\left(\int_{\mathbb{R}^n}|x|^{-qb}|u|^qdx\right)^{\frac{1}{q}},\quad\forall\; u\in D_a^p(\mathbb{R}^n), \end{equation*} where $S(p,a,b)$ is the sharp constant and $a,b,p,q$ satisfy the relations: \begin{equation*} 0\leq a<\frac{n-p}{p},\quad a\leq b

The recently emerging text-to-motion advances have spired numerous attempts for convenient and interactive human motion generation. Yet, existing methods are largely limited to generating body motions only without considering the rich two-hand motions, let alone handling various conditions like body dynamics or texts. To break the data bottleneck, we propose BOTH57M, a novel multi-modal dataset for two-hand motion generation. Our dataset includes accurate motion tracking for the human body and hands and provides pair-wised finger-level hand annotations and body descriptions. We further provide a strong baseline method, BOTH2Hands, for the novel task: generating vivid two-hand motions from both implicit body dynamics and explicit text prompts. We first warm up two parallel body-to-hand and text-to-hand diffusion models and then utilize the cross-attention transformer for motion blending. Extensive experiments and cross-validations demonstrate the effectiveness of our approach and dataset for generating convincing two-hand motions from the hybrid body-and-textual conditions. Our dataset and code will be disseminated to the community for future research., Comment: Accepted to CVPR 2024

In this paper, we investigate positive solutions to the following H\'enon-Sobolev critical system: $$ -\mathrm{div}(|x|^{-2a}\nabla u)=|x|^{-bp}|u|^{p-2}u+\nu\alpha|x|^{-bp}|u|^{\alpha-2}|v|^{\beta}u\quad\text{in }\mathbb{R}^n,$$ $$ -\mathrm{div}(|x|^{-2a}\nabla v)=|x|^{-bp}|v|^{p-2}v+\nu\beta|x|^{-bp}|u|^{\alpha}|v|^{\beta-2}v\quad\text{in }\mathbb{R}^n,$$ $$u,v\in D_a^{1,2}(\mathbb{R}^n),$$ where $n\geq 3,-\infty< a<\frac{n-2}{2},a\leq b0$ and $\alpha>1,\beta>1$ satisfying $\alpha+\beta=p$. Our findings are divided into two parts, according to the sign of the parameter $a$. For $a\geq 0$, we demonstrate that any positive solution $(u,v)$ is synchronized, indicating that $u$ and $v$ are constant multiples of positive solutions to the decoupled H\'enon equation: \begin{equation*} -\mathrm{div}(|x|^{-2a}\nabla w)=|x|^{-bp}|w|^{p-2}w. \end{equation*} For $a<0$ and $b>a$, we characterize all nonnegative ground states. Additionally, we study the nondegeneracy of nonnegative synchronized solutions. This work also delves into some general $k$-coupled H\'enon-Sobolev critical systems., Comment: 23 pages, all comments are welcome!

In this paper, we study the stability of fractional Sobolev trace inequality within both the functional and critical point settings. In the functional setting, we establish the following sharp estimate: $$C_{\mathrm{BE}}(n,m,\alpha)\inf_{v\in\mathcal{M}_{n,m,\alpha}}\left\Vert f-v\right\Vert_{D_\alpha(\mathbb{R}^n)}^2 \leq \left\Vert f\right\Vert_{D_\alpha(\mathbb{R}^n)}^2 - S(n,m,\alpha) \left\Vert\tau_mf\right\Vert_{L^{q}(\mathbb{R}^{n-m})}^2,$$ where $0\leq m< n$, $\frac{m}{2}<\alpha<\frac{n}{2}, q=\frac{2(n-m)}{n-2\alpha}$ and $\mathcal{M}_{n,m,\alpha}$ denotes the manifold of extremal functions. Additionally, We find an explicit bound for the stability constant $C_{\mathrm{BE}}$ and establish a compactness result ensuring the existence of minimizers. In the critical point setting, we investigate the validity of a sharp quantitative profile decomposition related to the Escobar trace inequality and establish a qualitative profile decomposition for the critical elliptic equation \begin{equation*} \Delta u= 0 \quad\text{in }\mathbb{R}_+^n,\quad\frac{\partial u}{\partial t}=-|u|^{\frac{2}{n-2}}u \quad\text{on }\partial\mathbb{R}_+^n. \end{equation*} We then derive the sharp stability estimate: $$ C_{\mathrm{CP}}(n,\nu)d(u,\mathcal{M}_{\mathrm{E}}^{\nu})\leq \left\Vert \Delta u +|u|^{\frac{2}{n-2}}u\right\Vert_{H^{-1}(\mathbb{R}_+^n)}, $$ where $\nu=1,n\geq 3$ or $\nu\geq2,n=3$ and $\mathcal{M}_{\mathrm{E}}^\nu$ represents the manifold consisting of $\nu$ weak-interacting Escobar bubbles. Through some refined estimates, we also give a strict upper bound for $C_{\mathrm{CP}}(n,1)$, which is $\frac{2}{n+2}$., Comment: 42 pages, all comments are welcome!

Scene Text Image Super-Resolution (STISR) aims to enhance the resolution and legibility of text within low-resolution (LR) images, consequently elevating recognition accuracy in Scene Text Recognition (STR). Previous methods predominantly employ discriminative Convolutional Neural Networks (CNNs) augmented with diverse forms of text guidance to address this issue. Nevertheless, they remain deficient when confronted with severely blurred images, due to their insufficient generation capability when little structural or semantic information can be extracted from original images. Therefore, we introduce RGDiffSR, a Recognition-Guided Diffusion model for scene text image Super-Resolution, which exhibits great generative diversity and fidelity even in challenging scenarios. Moreover, we propose a Recognition-Guided Denoising Network, to guide the diffusion model generating LR-consistent results through succinct semantic guidance. Experiments on the TextZoom dataset demonstrate the superiority of RGDiffSR over prior state-of-the-art methods in both text recognition accuracy and image fidelity.

We investigate the electronic and magnetic properties of the newly synthesized double perovskites Y$_{2}$NiIrO$_{6}$ and La$_{2}$NiIrO$_{6}$, using density functional calculations, crystal field theory, superexchange pictures, and Monte Carlo simulations. We find that both systems are antiferromagnetic (AFM) Mott insulators, with the high-spin Ni$^{2+}$ $t_{2g}$$^{6}e_{g}$$^{2}$ ($S=1$) and the low-spin Ir$^{4+}$ $t_{2g}$$^{5}$ ($S=1/2$) configurations. We address that their lattice distortion induces $t_{2g}$-$e_{g}$ orbital mixing and thus enables the normal Ni$^{+}$-Ir$^{5+}$ charge excitation with the electron hopping from the Ir `$t_{2g}$' to Ni `$e_g$' orbitals, which promotes the AFM Ni$^{2+}$-Ir$^{4+}$ coupling. Therefore, the increasing $t_{2g}$-$e_{g}$ mixing accounts for the enhanced $T_{\rm N}$ from the less distorted La$_{2}$NiIrO$_{6}$ to the more distorted Y$_{2}$NiIrO$_{6}$. Moreover, our test calculations find that in the otherwise ideally cubic Y$_{2}$NiIrO$_{6}$, the Ni$^{+}$-Ir$^{5+}$ charge excitation is forbidden, and only the abnormal Ni$^{3+}$-Ir$^{3+}$ excitation gives a weakly ferromagnetic (FM) behavior. Furthermore, we find that owing to the crystal field splitting, Hund exchange, and broad band formation in the highly coordinated fcc sublattice, Ir$^{4+}$ ions are not in the $j_{\rm eff}=1/2$ state but in the $S=1/2$ state carrying a finite orbital moment by spin-orbit coupling (SOC). This work clarifies the varying magnetism in Y$_{2}$NiIrO$_{6}$ and La$_{2}$NiIrO$_{6}$ associated with the lattice distortions., Comment: 7 pages, 7 figures, 1 table

We propose DISC-LawLLM, an intelligent legal system utilizing large language models (LLMs) to provide a wide range of legal services. We adopt legal syllogism prompting strategies to construct supervised fine-tuning datasets in the Chinese Judicial domain and fine-tune LLMs with legal reasoning capability. We augment LLMs with a retrieval module to enhance models' ability to access and utilize external legal knowledge. A comprehensive legal benchmark, DISC-Law-Eval, is presented to evaluate intelligent legal systems from both objective and subjective dimensions. Quantitative and qualitative results on DISC-Law-Eval demonstrate the effectiveness of our system in serving various users across diverse legal scenarios. The detailed resources are available at https://github.com/FudanDISC/DISC-LawLLM.

Hand action recognition is essential. Communication, human-robot interactions, and gesture control are dependent on it. Skeleton-based action recognition traditionally includes hands, which belong to the classes which remain challenging to correctly recognize to date. We propose a method specifically designed for hand action recognition which uses relative angular embeddings and local Spherical Harmonics to create novel hand representations. The use of Spherical Harmonics creates rotation-invariant representations which make hand action recognition even more robust against inter-subject differences and viewpoint changes. We conduct extensive experiments on the hand joints in the First-Person Hand Action Benchmark with RGB-D Videos and 3D Hand Pose Annotations, and on the NTU RGB+D 120 dataset, demonstrating the benefit of using Local Spherical Harmonics Representations. Our code is available at https://github.com/KathPra/LSHR_LSHT.

Monocular visual-inertial odometry (VIO) is a low-cost solution to provide high-accuracy, low-drifting pose estimation. However, it has been meeting challenges in vehicular scenarios due to limited dynamics and lack of stable features. In this paper, we propose Ground-VIO, which utilizes ground features and the specific camera-ground geometry to enhance monocular VIO performance in realistic road environments. In the method, the camera-ground geometry is modeled with vehicle-centered parameters and integrated into an optimization-based VIO framework. These parameters could be calibrated online and simultaneously improve the odometry accuracy by providing stable scale-awareness. Besides, a specially designed visual front-end is developed to stably extract and track ground features via the inverse perspective mapping (IPM) technique. Both simulation tests and real-world experiments are conducted to verify the effectiveness of the proposed method. The results show that our implementation could dramatically improve monocular VIO accuracy in vehicular scenarios, achieving comparable or even better performance than state-of-art stereo VIO solutions. The system could also be used for the auto-calibration of IPM which is widely used in vehicle perception. A toolkit for ground feature processing, together with the experimental datasets, would be made open-source (https://github.com/GREAT-WHU/gv_tools).

Energy spectroscopy is a powerful tool with diverse applications across various disciplines. The advent of programmable digital quantum simulators opens new possibilities for conducting spectroscopy on various models using a single device. Variational quantum-classical algorithms have emerged as a promising approach for achieving such tasks on near-term quantum simulators, despite facing significant quantum and classical resource overheads. Here, we experimentally demonstrate multi-level variational spectroscopy for fundamental many-body Hamiltonians using a superconducting programmable digital quantum simulator. By exploiting symmetries, we effectively reduce circuit depth and optimization parameters allowing us to go beyond the ground state. Combined with the subspace search method, we achieve full spectroscopy for a 4-qubit Heisenberg spin chain, yielding an average deviation of 0.13 between experimental and theoretical energies, assuming unity coupling strength. Our method, when extended to 8-qubit Heisenberg and transverse-field Ising Hamiltonians, successfully determines the three lowest energy levels. In achieving the above, we introduce a circuit-agnostic waveform compilation method that enhances the robustness of our simulator against signal crosstalk. Our study highlights symmetry-assisted resource efficiency in variational quantum algorithms and lays the foundation for practical spectroscopy on near-term quantum simulators, with potential applications in quantum chemistry and condensed matter physics.

The NLI4CT task aims to entail hypotheses based on Clinical Trial Reports (CTRs) and retrieve the corresponding evidence supporting the justification. This task poses a significant challenge, as verifying hypotheses in the NLI4CT task requires the integration of multiple pieces of evidence from one or two CTR(s) and the application of diverse levels of reasoning, including textual and numerical. To address these problems, we present a multi-granularity system for CTR-based textual entailment and evidence retrieval in this paper. Specifically, we construct a Multi-granularity Inference Network (MGNet) that exploits sentence-level and token-level encoding to handle both textual entailment and evidence retrieval tasks. Moreover, we enhance the numerical inference capability of the system by leveraging a T5-based model, SciFive, which is pre-trained on the medical corpus. Model ensembling and a joint inference method are further utilized in the system to increase the stability and consistency of inference. The system achieves f1-scores of 0.856 and 0.853 on textual entailment and evidence retrieval tasks, resulting in the best performance on both subtasks. The experimental results corroborate the effectiveness of our proposed method. Our code is publicly available at https://github.com/THUMLP/NLI4CT., Comment: Accepted by SemEval2023

Graph Convolutional Networks (GCNs) have long defined the state-of-the-art in skeleton-based action recognition, leveraging their ability to unravel the complex dynamics of human joint topology through the graph's adjacency matrix. However, an inherent flaw has come to light in these cutting-edge models: they tend to optimize the adjacency matrix jointly with the model weights. This process, while seemingly efficient, causes a gradual decay of bone connectivity data, culminating in a model indifferent to the very topology it sought to map. As a remedy, we propose a threefold strategy: (1) We forge an innovative pathway that encodes bone connectivity by harnessing the power of graph distances. This approach preserves the vital topological nuances often lost in conventional GCNs. (2) We highlight an oft-overlooked feature - the temporal mean of a skeletal sequence, which, despite its modest guise, carries highly action-specific information. (3) Our investigation revealed strong variations in joint-to-joint relationships across different actions. This finding exposes the limitations of a single adjacency matrix in capturing the variations of relational configurations emblematic of human movement, which we remedy by proposing an efficient refinement to Graph Convolutions (GC) - the BlockGC. This evolution slashes parameters by a substantial margin (above 40%), while elevating performance beyond original GCNs. Our full model, the BlockGCN, establishes new standards in skeleton-based action recognition for small model sizes. Its high accuracy, notably on the large-scale NTU RGB+D 120 dataset, stand as compelling proof of the efficacy of BlockGCN.

As the basis for generating multi-particle quantum correlations, inter-particle interaction plays a crucial role in collective quantum phenomena, quantum phase transitions, and quantum information processing. It can profoundly alter the band structure of quantum many-body systems and give rise to exotic topological phenomena. Conventional topological pumping, which has been well demonstrated in driven linear or noninteracting systems, may break down in the presence of strong interaction. However, the interplay between band topology and interaction could also induce emergent topological pumping of interacting particles, but its experimental realization has proven challenging. Here we demonstrate interaction-induced topological pumping in a solid-state quantum system comprising an array of 36 superconducting qubits. With strong interaction inherent in the qubits and site-resolved controllability of the lattice potential and hopping strength, we realize the topological Thouless pumping of single and two bounded particles. Beyond these topological phenomena with linear or noninteracting counterparts, we also observe topologically resonant tunneling and asymmetric edge-state transport of interacting particles. Our work creates a paradigm for multi-particle topological effects, and provides a new pathway to the study of exotic topological phenomena, many-body quantum transport, and quantum information transfer., Comment: 8+29 pages, 4+24 figures

Scaling is now a key challenge in superconducting quantum computing. One solution is to build modular systems in which smaller-scale quantum modules are individually constructed and calibrated, and then assembled into a larger architecture. This, however, requires the development of suitable interconnects. Here, we report low-loss interconnects based on pure aluminium coaxial cables and on-chip impedance transformers featuring quality factors up to $8.1 \times 10^5$, which is comparable to the performance of our transmon qubits fabricated on single-crystal sapphire substrate. We use these interconnects to link five quantum modules with inter-module quantum state transfer and Bell state fidelities up to 99\%. To benchmark the overall performance of the processor, we create maximally-entangled, multi-qubit Greenberger-Horne-Zeilinger (GHZ) states. The generated inter-module four-qubit GHZ state exhibits 92.0\% fidelity. We also entangle up to 12 qubits in a GHZ state with $55.8 \pm 1.8\%$ fidelity, which is above the genuine multipartite entanglement threshold of 1/2. These results represent a viable modular approach for large-scale superconducting quantum processors.

Skeleton-based action recognition aims to recognize human actions given human joint coordinates with skeletal interconnections. By defining a graph with joints as vertices and their natural connections as edges, previous works successfully adopted Graph Convolutional networks (GCNs) to model joint co-occurrences and achieved superior performance. More recently, a limitation of GCNs is identified, i.e., the topology is fixed after training. To relax such a restriction, Self-Attention (SA) mechanism has been adopted to make the topology of GCNs adaptive to the input, resulting in the state-of-the-art hybrid models. Concurrently, attempts with plain Transformers have also been made, but they still lag behind state-of-the-art GCN-based methods due to the lack of structural prior. Unlike hybrid models, we propose a more elegant solution to incorporate the bone connectivity into Transformer via a graph distance embedding. Our embedding retains the information of skeletal structure during training, whereas GCNs merely use it for initialization. More importantly, we reveal an underlying issue of graph models in general, i.e., pairwise aggregation essentially ignores the high-order kinematic dependencies between body joints. To fill this gap, we propose a new self-attention (SA) mechanism on hypergraph, termed Hypergraph Self-Attention (HyperSA), to incorporate intrinsic higher-order relations into the model. We name the resulting model Hyperformer, and it beats state-of-the-art graph models w.r.t. accuracy and efficiency on NTU RGB+D, NTU RGB+D 120, and Northwestern-UCLA datasets.

Skeleton-based action recognition has recently received considerable attention. Current approaches to skeleton-based action recognition are typically formulated as one-hot classification tasks and do not fully exploit the semantic relations between actions. For example, "make victory sign" and "thumb up" are two actions of hand gestures, whose major difference lies in the movement of hands. This information is agnostic from the categorical one-hot encoding of action classes but could be unveiled from the action description. Therefore, utilizing action description in training could potentially benefit representation learning. In this work, we propose a Generative Action-description Prompts (GAP) approach for skeleton-based action recognition. More specifically, we employ a pre-trained large-scale language model as the knowledge engine to automatically generate text descriptions for body parts movements of actions, and propose a multi-modal training scheme by utilizing the text encoder to generate feature vectors for different body parts and supervise the skeleton encoder for action representation learning. Experiments show that our proposed GAP method achieves noticeable improvements over various baseline models without extra computation cost at inference. GAP achieves new state-of-the-arts on popular skeleton-based action recognition benchmarks, including NTU RGB+D, NTU RGB+D 120 and NW-UCLA. The source code is available at https://github.com/MartinXM/GAP., Comment: Accepted by ICCV23

Gate-based quantum computation has been extensively investigated using quantum circuits based on qubits. In many cases, such qubits are actually made out of multilevel systems but with only two states being used for computational purpose. While such a strategy has the advantage of being in line with the common binary logic, it in some sense wastes the ready-for-use resources in the large Hilbert space of these intrinsic multi-dimensional systems. Quantum computation beyond qubits (e.g., using qutrits or qudits) has thus been discussed and argued to be more efficient than its qubit counterpart in certain scenarios. However, one of the essential elements for qutrit-based quantum computation, two-qutrit quantum gate, remains a major challenge. In this work, we propose and demonstrate a highly efficient and scalable two-qutrit quantum gate in superconducting quantum circuits. Using a tunable coupler to control the cross-Kerr coupling between two qutrits, our scheme realizes a two-qutrit conditional phase gate with fidelity 89.3% by combining simple pulses applied to the coupler with single-qutrit operations. We further use such a two-qutrit gate to prepare an EPR state of two qutrits with a fidelity of 95.5%. Our scheme takes advantage of a tunable qutrit-qutrit coupling with a large on:off ratio. It therefore offers both high efficiency and low cross talk between qutrits, thus being friendly for scaling up. Our work constitutes an important step towards scalable qutrit-based quantum computation., Comment: 15 pages, 12 figures

Recently, transformers have shown great potential in image classification and established state-of-the-art results on the ImageNet benchmark. However, compared to CNNs, transformers converge slowly and are prone to overfitting in low-data regimes due to the lack of spatial inductive biases. Such spatial inductive biases can be especially beneficial since the 2D structure of an input image is not well preserved in transformers. In this work, we present Spatial Prior-enhanced Self-Attention (SP-SA), a novel variant of vanilla Self-Attention (SA) tailored for vision transformers. Spatial Priors (SPs) are our proposed family of inductive biases that highlight certain groups of spatial relations. Unlike convolutional inductive biases, which are forced to focus exclusively on hard-coded local regions, our proposed SPs are learned by the model itself and take a variety of spatial relations into account. Specifically, the attention score is calculated with emphasis on certain kinds of spatial relations at each head, and such learned spatial foci can be complementary to each other. Based on SP-SA we propose the SP-ViT family, which consistently outperforms other ViT models with similar GFlops or parameters. Our largest model SP-ViT-L achieves a record-breaking 86.3% Top-1 accuracy with a reduction in the number of parameters by almost 50% compared to previous state-of-the-art model (150M for SP-ViT-L vs 271M for CaiT-M-36) among all ImageNet-1K models trained on 224x224 and fine-tuned on 384x384 resolution w/o extra data.

Hybrid transition metal oxides continue to attract attention due to their multiple degrees of freedom ($e.g.$, lattice, charge, spin, and orbital) and versatile properties. Here we investigate the magnetic and electronic properties of the newly synthesized double perovskite Ba$_2$NiIrO$_6$, using crystal field theory, superexchange model analysis, density functional calculations, and parallel tempering Monte Carlo (PTMC) simulations. Our results indicate that Ba$_2$NiIrO$_6$ has the Ni$^{2+}$ ($t_{2g}^{6}e_{g}^{2}$)-Ir$^{6+}$ ($t_{2g}^{3}$) charge states. The first nearest-neighboring (1NN) Ni$^{2+}$-Ir$^{6+}$ ions prefer a ferromagnetic (FM) coupling as expected from the Goodenough-Kanamori-Anderson rules, which contradicts the experimental antiferromagnetic (AF) order in Ba$_2$NiIrO$_6$. We find that the strong 2NN AF couplings are frustrated in the fcc sublattices, and they play a major role in determining the observed AF ground state. We also prove that the $J_{\rm eff}$ = 3/2 and $J_{\rm eff}$ = 1/2 states induced by spin-orbit coupling, which would be manifested in low-dimensional (e.g., layered) iridates, are however not the case for cubic Ba$_2$NiIrO$_6$. Our PTMC simulations show that when the long-range (2NN and 3NN) AF interactions are included, an AF transition with $T_{\rm N}$ = 66 K would be obtained and it is well comparable with the experimental 51 K. Meanwhile, we propose a possible 2$\times$2$\times$2 noncollinear AF structure for Ba$_2$NiIrO$_6$., Comment: 6 pages, 8 figures, 1 table