arXiv subjects
Publications and source records attributed to Kai Xu.
We study the derived category of coherent sheaves on various versions of moduli space of vector bundles on curves by the Borel-Weil-Bott theory for loop groups and $Θ$-stratification, and construct a semiorthogonal decomposition with blocks given by symmetric powers of the curve.
The masses of tetraquark states of all $qc\bar q \bar c$ and $cc\bar c \bar c$ quark configurations are evaluated in a constituent quark model, where the Cornell-like potential and one-gluon exchange spin-spin coupling are employed. All model parameters are predetermined by comparing the theoretical and experimental masses of light, charmed and bottom mesons. The theoretical predictions of the charmoniumlike tetraquarks are compared with the observed $XYZ$ states, and one tentative assignment is suggested. The work suggests that the $X(6900)$ observed by LHCb is likely to be the first radial excited fully-charm tetraquark state with $J^{PC} = 1^{+-}$ in the $\bar 3_c \otimes 3_c$ configuration, and the ground and second radial excited states of fully-charm tetraquark are around $6494$ and $7253$ MeV respectively.
Holonomies, arising from non-Abelian geometric transformations of quantum states in Hilbert space, offer a promising way for quantum computation. These holonomies are not commutable and thus can be used for the realization of a universal set of quantum logic gates, where the global geometric feature may result in some noise-resilient advantages. Here we report the first on-chip realization of a non-Abelian geometric controlled-Not gate in a superconducting circuit, which is a building block for constructing a holonomic quantum computer. The conditional dynamics is achieved in an all-to-all connected architecture involving multiple frequency-tunable superconducting qubits controllably coupled to a resonator; a holonomic gate between any two qubits can be implemented by tuning their frequencies on resonance with the resonator and applying a two-tone drive to one of them. This gate represents an important step towards the all-geometric realization of scalable quantum computation on a superconducting platform.
No-cloning theorem forbids perfect cloning of an unknown quantum state. A universal quantum cloning machine (UQCM), capable of producing two copies of any input qubit with the optimal fidelity, is of fundamental interest and has applications in quantum information processing. This is enabled by delicately tailored nonclassical correlations between the input qubit and the copying qubits, which distinguish the UQCM from a classical counterpart, but whose experimental demonstrations are still lacking. We here implement the UQCM in a superconducting circuit, and investigate these correlations. The measured entanglements well agree with our theoretical prediction that they are independent of the input state and thus constitute a universal quantum behavior of the UQCM that was not previously revealed. Another feature of our experiment is the realization of deterministic and individual cloning, in contrast to previously demonstrated UQCMs, which either were probabilistic or did not constitute true cloning of individual qubits.
Online reconstruction based on RGB-D sequences has thus far been restrained to relatively slow camera motions (<1m/s). Under very fast camera motion (e.g., 3m/s), the reconstruction can easily crumble even for the state-of-the-art methods. Fast motion brings two challenges to depth fusion: 1) the high nonlinearity of camera pose optimization due to large inter-frame rotations and 2) the lack of reliably trackable features due to motion blur. We propose to tackle the difficulties of fast-motion camera tracking in the absence of inertial measurements using random optimization, in particular, the Particle Filter Optimization (PFO). To surmount the computation-intensive particle sampling and update in standard PFO, we propose to accelerate the randomized search via updating a particle swarm template (PST). PST is a set of particles pre-sampled uniformly within the unit sphere in the 6D space of camera pose. Through moving and rescaling the pre-sampled PST guided by swarm intelligence, our method is able to drive tens of thousands of particles to locate and cover a good local optimum extremely fast and robustly. The particles, representing candidate poses, are evaluated with a fitness function defined based on depth-model conformance. Therefore, our method, being depth-only and correspondence-free, mitigates the motion blur impediment as ToF-based depths are often resilient to motion blur. Thanks to the efficient template-based particle set evolution and the effective fitness function, our method attains good quality pose tracking under fast camera motion (up to 4m/s) in a realtime framerate without including loop closure or global pose optimization. Through extensive evaluations on public datasets of RGB-D sequences, especially on a newly proposed benchmark of fast camera motion, we demonstrate the significant advantage of our method over the state of the arts.
Hamiltonian Monte Carlo (HMC) is a popular sampling method in Bayesian inference. Recently, Heng & Jacob (2019) studied Metropolis HMC with couplings for unbiased Monte Carlo estimation, establishing a generic parallelizable scheme for HMC. However, in practice a different HMC method, multinomial HMC, is considered as the go-to method, e.g. as part of the no-U-turn sampler. In multinomial HMC, proposed states are not limited to end-points as in Metropolis HMC; instead points along the entire trajectory can be proposed. In this paper, we establish couplings for multinomial HMC, based on optimal transport for multinomial sampling in its transition. We prove an upper bound for the meeting time - the time it takes for the coupled chains to meet - based on the notion of local contractivity. We evaluate our methods using three targets: 1,000 dimensional Gaussians, logistic regression and log-Gaussian Cox point processes. Compared to Heng & Jacob (2019), coupled multinomial HMC generally attains a smaller meeting time, and is more robust to choices of step sizes and trajectory lengths, which allows re-use of existing adaptation methods for HMC. These improvements together paves the way for a wider and more practical use of coupled HMC methods.
Recently, various convolutions based on continuous or discrete kernels for point cloud processing have been widely studied, and achieve impressive performance in many applications, such as shape classification, scene segmentation and so on. However, they still suffer from some drawbacks. For continuous kernels, the inaccurate estimation of the kernel weights constitutes a bottleneck for further improving the performance; while for discrete ones, the kernels represented as the points located in the 3D space are lack of rich geometry information. In this work, rather than defining a continuous or discrete kernel, we directly embed convolutional kernels into the learnable potential fields, giving rise to potential convolution. It is convenient for us to define various potential functions for potential convolution which can generalize well to a wide range of tasks. Specifically, we provide two simple yet effective potential functions via point-wise convolution operations. Comprehensive experiments demonstrate the effectiveness of our method, which achieves superior performance on the popular 3D shape classification and scene segmentation benchmarks compared with other state-of-the-art point convolution methods.
Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterises the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalisation of the RSP with respect to nonlinear observables, and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, here we report the characterisation of multiparticle entangled states generated during its nonlinear dynamics. First, selecting 10 qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89$^{+0.28}_{-0.29}$ dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.
The Bloch oscillation (BO) and Wannier-Stark localization (WSL) are fundamental concepts about metal-insulator transitions in condensed matter physics. These phenomena have also been observed in semiconductor superlattices and simulated in platforms such as photonic waveguide arrays and cold atoms. Here, we report experimental investigation of BOs and WSL simulated with a 5-qubit programmable superconducting processor, of which the effective Hamiltonian is an isotropic $XY$ spin chain. When applying a linear potential to the system by properly tuning all individual qubits, we observe that the propagation of a single spin on the chain is suppressed. It tends to oscillate near the neighborhood of their initial positions, which demonstrates the characteristics of BOs and WSL. We verify that the WSL length is inversely correlated to the potential gradient. Benefiting from the precise single-shot simultaneous readout of all qubits in our experiments, we can also investigate the thermal transport, which requires the joint measurement of more than one qubits. The experimental results show that, as an essential characteristic for BOs and WSL, the thermal transport is also blocked under a linear potential. Our experiment would be scalable to more superconducting qubits for simulating various of out-of-equilibrium problems in quantum many-body systems.
We introduce the concept of geometric stability to the problem of 6D object pose estimation and propose to learn pose inference based on geometrically stable patches extracted from observed 3D point clouds. According to the theory of geometric stability analysis, a minimal set of three planar/cylindrical patches are geometrically stable and determine the full 6DoFs of the object pose. We train a deep neural network to regress 6D object pose based on geometrically stable patch groups via learning both intra-patch geometric features and inter-patch contextual features. A subnetwork is jointly trained to predict per-patch poses. This auxiliary task is a relaxation of the group pose prediction: A single patch cannot determine the full 6DoFs but is able to improve pose accuracy in its corresponding DoFs. Working with patch groups makes our method generalize well for random occlusion and unseen instances. The method is easily amenable to resolve symmetry ambiguities. Our method achieves the state-of-the-art results on public benchmarks compared not only to depth-only but also to RGBD methods. It also performs well in category-level pose estimation.
With a view toward a fracton theory in condensed matter, we introduce a higher-moment polynomial degree-p global symmetry, acting on complex scalar/vector/tensor fields (e.g., ordinary or vector global symmetry for p$=0$ and p$=1$ respectively). We relate this higher-moment global symmetry of $n$-dimensional space, to a lower degree (either ordinary or higher-moment, e.g., degree-(p-$\ell$)) subdimensional or subsystem global symmetry on layers of $(n-\ell)$-submanifolds. These submanifolds are algebraic affine varieties (i.e., solutions of polynomials). The structure of layers of submanifolds as subvarieties can be studied via mathematical tools of embedding, foliation, and algebraic geometry. We also generalize Noether's theorem for this higher-moment polynomial global symmetry. We can promote the higher-moment global symmetry to a local symmetry, and derive a new family of higher-rank-m symmetric tensor gauge theory by gauging, with m = p$+1$. By further gauging a discrete $\mathbb{Z}_2^C$ charge conjugation (particle-hole) symmetry, we derive a new general class of rank-m tensor non-abelian gauge field theory (the gauge structure is non-commutative thus non-abelian but not an ordinary group): a hybrid class of (symmetric or non-symmetric) higher-rank-m tensor gauge theory and anti-symmetric tensor topological field theory, generalizing [arXiv:1909.13879], interplaying between gapless and gapped sectors.
Quantum speed limit time (QSLT) can be used to characterize the intrinsic minimal time interval for a quantum system evolving from an initial state to a target state. We investigate the QSLT of the open system in Schwarzschild space-time. We show that, in some typical noisy channels,the Hawking effect can be beneficial to the evolution of the system. For an initial entangled state, the evolution speed of the system can be enhanced in the depolarizing, bit flip, and bit-phase flip channels as the Hawking temperature increases, which are in sharp contrast to the phase flip channel. Moreover, the optimal initial entanglement exists in other noise channels except the phase flip channel, which minimizes the QSLT of the system and thus leads to the maximum evolution speed of the system.
The equilibration of a trivalent polygonal network in two dimensions (2D) is a universal phenomenon in nature, but the underlying mathematical mechanism remains unclear. In this study, a relaxation algorithm based on a simple geometrical rule was developed to simulate the equilibration. The proposed algorithm was implemented in Python language. The simulated relaxation changed the polygonal cell of the Voronoi network from an ellipse's inscribed polygon toward the ellipse's maximal inscribed polygon. Meanwhile, the Aboav-Weaire's law, which describes the neighboring relationship between cells, still holds statistically. The succeed of simulation strongly supports the ellipse packing hypothesis that was proposed to explain the dynamic behaviors of a trivalent 2D structure. The simulation results also showed that the edge of large cells tends to be shorter than edges of small cells, and vice versa. In addition, the relaxation increases the area and edge length of large cells, and it decreases the area and edge length of small cells. The pattern of changes in the area of different-edged cells due to relaxation is almost the same as the growth pattern described by the von-Neumann-Mullins law. The results presented in this work can help to understand the mathematical mechanisms of the dynamic behaviors of trivalent 2D structures.
We perform a systematic study of the spin polarization of hyperons in heavy-ion collisions using the MUSIC hydrodynamic model with A Multi-Phase Transport (AMPT) pre-equilibrium dynamics. Our model calculations nicely describe the measured collision-energy, centrality, rapidity, and $p_T$ dependence of $Λ$ polarization. We also study and predict the global spin polarization of $Ξ^-$ and $Ω^-$ as a function of collision energy, which provides a baseline for the studies of the magnetic moment, spin, and mass dependence of the spin polarization. For the local spin polarization, we calculate the radial and azimuthal components of the transverse $Λ$ polarization and find specific modulating behavior which could reflect the circular vortical structure. However, our model fails to describe the azimuthal-angle dependence of the longitudinal and transverse $Λ$ polarization, which indicates that the hydrodynamic framework with the spin Cooper-Frye formula under the assumption of thermal equilibrium of spin degree of freedom needs to be improved.
Determining the value of basketball players through analyzing the players' behavior is important for the managers of modern basketball teams. However, conventional methods always utilize isolated statistical data, leading to ineffective and inaccurate evaluations. Existing models based on dynamic network theory offer major improvements to the results of such evaluations, but said models remain imprecise because they focus merely on evaluating the values of individual players rather than considering them within their current teams. To solve this problem, we propose an analysis and evaluation model based on networks and a hidden Markov model. To the best of our knowledge, we are the first to combine a network form representing the players who are playing with the use of a hidden Markov model to mine the network and generate the desired results. Applying our approach to SportVU data collected from the National Basketball Association shows that this analysis and evaluation model can effectively analyze the performance of each player in a game and provides an assistive tool for team managers.
Without a shape-aware response, it is hard to characterize the 3D geometry of a point cloud efficiently with a compact set of kernels. In this paper, we advocate the use of Hausdorff distance as a shape-aware distance measure for calculating point convolutional responses. The technique we present, coined Hausdorff Point Convolution (HPC), is shape-aware. We show that HPC constitutes a powerful point feature learning with a rather compact set of only four types of geometric priors as kernels. We further develop a HPC-based deep neural network (HPC-DNN). Task-specific learning can be achieved by tuning the network weights for combining the shortest distances between input and kernel point sets. We also realize hierarchical feature learning by designing a multi-kernel HPC for multi-scale feature encoding. Extensive experiments demonstrate that HPC-DNN outperforms strong point convolution baselines (e.g., KPConv), achieving 2.8% mIoU performance boost on S3DIS and 1.5% on SemanticKITTI for semantic segmentation task.
Autonomous 3D acquisition of outdoor environments poses special challenges. Different from indoor scenes, where the room space is delineated by clear boundaries and separations (e.g., walls and furniture), an outdoor environment is spacious and unbounded (thinking of a campus). Therefore, unlike for indoor scenes where the scanning effort is mainly devoted to the discovery of boundary surfaces, scanning an open and unbounded area requires actively delimiting the extent of scanning region and dynamically planning a traverse path within that region. Thus, for outdoor scenes, we formulate the planning of an energy-efficient autonomous scanning through a discrete-continuous optimization of robot scanning paths. The discrete optimization computes a topological map, through solving an online traveling sales problem (Online TSP), which determines the scanning goals and paths on-the-fly. The dynamic goals are determined as a collection of visit sites with high reward of visibility-to-unknown. A visit graph is constructed via connecting the visit sites with edges weighted by traversing cost. This topological map evolves as the robot scans via deleting outdated sites that are either visited or become rewardless and inserting newly discovered ones. The continuous part optimizes the traverse paths geometrically between two neighboring visit sites via maximizing the information gain of scanning along the paths. The discrete and continuous processes alternate until the traverse cost of the current graph exceeds the remaining energy capacity of the robot. Our approach is evaluated with both synthetic and field tests, demonstrating its effectiveness and advantages over alternatives. The project is at http://vcc.szu.edu.cn/research/2020/Husky, and the codes are available at https://github.com/alualu628628/Autonomous-Outdoor-Scanning-via-Online-Topological-and-Geometric-Path-Optimization.
We introduce AdaCoSeg, a deep neural network architecture for adaptive co-segmentation of a set of 3D shapes represented as point clouds. Differently from the familiar single-instance segmentation problem, co-segmentation is intrinsically contextual: how a shape is segmented can vary depending on the set it is in. Hence, our network features an adaptive learning module to produce a consistent shape segmentation which adapts to a set. Specifically, given an input set of unsegmented shapes, we first employ an offline pre-trained part prior network to propose per-shape parts. Then, the co-segmentation network iteratively and} jointly optimizes the part labelings across the set subjected to a novel group consistency loss defined by matrix ranks. While the part prior network can be trained with noisy and inconsistently segmented shapes, the final output of AdaCoSeg is a consistent part labeling for the input set, with each shape segmented into up to (a user-specified) K parts. Overall, our method is weakly supervised, producing segmentations tailored to the test set, without consistent ground-truth segmentations. We show qualitative and quantitative results from AdaCoSeg and evaluate it via ablation studies and comparisons to state-of-the-art co-segmentation methods.