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With the rapid advancements of large-scale text-to-image diffusion models, various practical applications have emerged, bringing significant convenience to society. However, model developers may misuse the unauthorized data to train diffusion models. These data are at risk of being memorized by the models, thus potentially violating citizens' privacy rights. Therefore, in order to judge whether a specific image is utilized as a member of a model's training set, Membership Inference Attack (MIA) is proposed to serve as a tool for privacy protection. Current MIA methods predominantly utilize pixel-wise comparisons as distinguishing clues, considering the pixel-level memorization characteristic of diffusion models. However, it is practically impossible for text-to-image models to memorize all the pixel-level information in massive training sets. Therefore, we move to the more advanced structure-level memorization. Observations on the diffusion process show that the structures of members are better preserved compared to those of nonmembers, indicating that diffusion models possess the capability to remember the structures of member images from training sets. Drawing on these insights, we propose a simple yet effective MIA method tailored for text-to-image diffusion models. Extensive experimental results validate the efficacy of our approach. Compared to current pixel-level baselines, our approach not only achieves state-of-the-art performance but also demonstrates remarkable robustness against various distortions.

In this paper, we study numerical approximations of the ground states in finite temperature density functional theory. We formulate the problem with respect to the density matrices and justify the convergence of the finite dimensional approximations. Moreover, we provide an optimal a priori error estimate under some mild assumptions and present some numerical experiments to support the theory., Comment: 20 pages, 6 figures

This paper is concerned with $\textit{ab initio}$ crystal structure relaxation under a fixed unit cell volume, which is a step in calculating the static equations of state and forms the basis of thermodynamic property calculations for materials. The task can be formulated as an energy minimization with a determinant constraint. Widely used line minimization-based methods (e.g., conjugate gradient method) lack both efficiency and convergence guarantees due to the nonconvex nature of the feasible region as well as the significant differences in the curvatures of the potential energy surface with respect to atomic and lattice components. To this end, we propose a projected gradient descent algorithm named PANBB. It is equipped with (i) search direction projections onto the tangent spaces of the nonconvex feasible region for lattice vectors, (ii) distinct curvature-aware initial trial step sizes for atomic and lattice updates, and (iii) a nonrestrictive line minimization criterion as the stopping rule for the inner loop. It can be proved that PANBB favors theoretical convergence to equilibrium states. Across a benchmark set containing 223 structures from various categories, PANBB achieves average speedup factors of approximately 1.41 and 1.45 over the conjugate gradient method and direct inversion in the iterative subspace implemented in off-the-shelf simulation software, respectively. Moreover, it normally converges on all the systems, manifesting its unparalleled robustness. As an application, we calculate the static equations of state for the high-entropy alloy AlCoCrFeNi, which remains elusive owing to 160 atoms representing both chemical and magnetic disorder and the strong local lattice distortion. The results are consistent with the previous calculations and are further validated by experimental thermodynamic data., Comment: 13 pages, 10 figures, 1 table

Perturbation theory (PT) might be one of the most powerful and fruitful tools for both physicists and chemists, which has led to a wide variety of applications. Over the past decades, advances in quantum computing provide opportunities for alternatives to classical methods. Recently, a general quantum circuit estimating the low order PT corrections has been proposed. In this article, we revisit the quantum circuits for PT calculations, and develop the methods for higher order PT corrections of eigenenergy, especially the 3rd and 4th order corrections. We present the feasible quantum circuit to estimate each term in these PT corrections. There are two the fundamental operations in the proposed circuit. One approximates the perturbation terms, the other approximates the inverse of unperturbed energy difference. The proposed method can be generalized to higher order PT corrections., Comment: 10 pages, 3 figures

A method was proposed for the point cloud-based registration and image fusion between cardiac single photon emission computed tomography (SPECT) myocardial perfusion images (MPI) and cardiac computed tomography angiograms (CTA). Firstly, the left ventricle (LV) epicardial regions (LVERs) in SPECT and CTA images were segmented by using different U-Net neural networks trained to generate the point clouds of the LV epicardial contours (LVECs). Secondly, according to the characteristics of cardiac anatomy, the special points of anterior and posterior interventricular grooves (APIGs) were manually marked in both SPECT and CTA image volumes. Thirdly, we developed an in-house program for coarsely registering the special points of APIGs to ensure a correct cardiac orientation alignment between SPECT and CTA images. Fourthly, we employed ICP, SICP or CPD algorithm to achieve a fine registration for the point clouds (together with the special points of APIGs) of the LV epicardial surfaces (LVERs) in SPECT and CTA images. Finally, the image fusion between SPECT and CTA was realized after the fine registration. The experimental results showed that the cardiac orientation was aligned well and the mean distance error of the optimal registration method (CPD with affine transform) was consistently less than 3 mm. The proposed method could effectively fuse the structures from cardiac CTA and SPECT functional images, and demonstrated a potential in assisting in accurate diagnosis of cardiac diseases by combining complementary advantages of the two imaging modalities.

The generalized stacking-fault energy (GSFE) is the fundamental but key parameter for the plastic deformation of materials. We perform first-principles calculations by full-potential linearized augmented planewave (FLAPW) method to evaluate the GSFE based on the single-shift and triple-shift supercell models. Different degrees of defects are introduced in the two models, thereby affecting the convergence of the self-consistent field (SCF) iterations. We present an adaptive preconditioning scheme which can identify the long-wavelength divergence behavior of the Jacobian during the SCF iteration and automatically switch on the Kerker preconditioning to accelerate the convergence. We implement this algorithm in Elk-7.2.42 package and calculate the GSFE curves for Al, Cu, and Si (111) plane <-1-12> direction. We found that the single-shift and triple-shift supercell models have equivalent calculation accuracy and are within the experimental data uncertainty. For computational efficiency, the triple-shift supercell model is preferable due to its better convergence, exhibiting lower degree of defect compared to the single-shift supercell model., Comment: 10 pages, 8 figures

Session-based recommendation (SBR) aims to predict the next item at a certain time point based on anonymous user behavior sequences. Existing methods typically model session representation based on simple item transition information. However, since session-based data consists of limited users' short-term interactions, modeling session representation by capturing fixed item transition information from a single dimension suffers from data sparsity. In this paper, we propose a novel contrastive multi-level graph neural networks (CM-GNN) to better exploit complex and high-order item transition information. Specifically, CM-GNN applies local-level graph convolutional network (L-GCN) and global-level network (G-GCN) on the current session and all the sessions respectively, to effectively capture pairwise relations over all the sessions by aggregation strategy. Meanwhile, CM-GNN applies hyper-level graph convolutional network (H-GCN) to capture high-order information among all the item transitions. CM-GNN further introduces an attention-based fusion module to learn pairwise relation-based session representation by fusing the item representations generated by L-GCN and G-GCN. CM-GNN averages the item representations obtained by H-GCN to obtain high-order relation-based session representation. Moreover, to convert the high-order item transition information into the pairwise relation-based session representation, CM-GNN maximizes the mutual information between the representations derived from the fusion module and the average pool layer by contrastive learning paradigm. We conduct extensive experiments on multiple widely used benchmark datasets to validate the efficacy of the proposed method. The encouraging results demonstrate that our proposed method outperforms the state-of-the-art SBR techniques.

Molecular dynamics simulations have emerged as a potent tool for investigating the physical properties and kinetic behaviors of materials at the atomic scale, particularly in extreme conditions. Ab initio accuracy is now achievable with machine learning based interatomic potentials. With recent advancements in high-performance computing, highly accurate and large-scale simulations become feasible. This study introduces TensorMD, a new machine learning interatomic potential (MLIP) model that integrates physical principles and tensor diagrams. The tensor formalism provides a more efficient computation and greater flexibility for use with other scientific codes. Additionally, we proposed several portable optimization strategies and developed a highly optimized version for the new Sunway supercomputer. Our optimized TensorMD can achieve unprecedented performance on the new Sunway, enabling simulations of up to 52 billion atoms with a time-to-solution of 31 ps/step/atom, setting new records for HPC + AI + MD.

Optically addressable spin defects in three-dimensional (3D) crystals and two-dimensional (2D) van der Waals (vdW) materials are revolutionizing nanoscale quantum sensing. Spin defects in one-dimensional (1D) vdW nanotubes will provide unique opportunities due to their small sizes in two dimensions and absence of dangling bonds on side walls. However, optically detected magnetic resonance of localized spin defects in a nanotube has not been observed. Here, we report the observation of single spin color centers in boron nitride nanotubes (BNNTs) at room temperature. Our findings suggest that these BNNT spin defects possess a spin $S=1/2$ ground state without an intrinsic quantization axis, leading to orientation-independent magnetic field sensing. We harness this unique feature to observe anisotropic magnetization of a 2D magnet in magnetic fields along orthogonal directions, a challenge for conventional spin $S=1$ defects such as diamond nitrogen-vacancy centers. Additionally, we develop a method to deterministically transfer a BNNT onto a cantilever and use it to demonstrate scanning probe magnetometry. Further refinement of our approach will enable atomic scale quantum sensing of magnetic fields in any direction., Comment: 9 pages, 5 figures

Levitated diamond particles in high vacuum with internal spin qubits have been proposed for exploring macroscopic quantum mechanics, quantum gravity, and precision measurements. The coupling between spins and particle rotation can be utilized to study quantum geometric phase, create gyroscopes and rotational matter-wave interferometers. However, previous efforts in levitated diamonds struggled with vacuum level or spin state readouts. To address these gaps, we fabricate an integrated surface ion trap with multiple stabilization electrodes. This facilitates on-chip levitation and, for the first time, optically detected magnetic resonance measurements of a nanodiamond levitated in high vacuum. The internal temperature of our levitated nanodiamond remains moderate below $10^{-5}$ Torr. Impressively, we have driven a nanodiamond to rotate up to 20 MHz ($1.2 \times 10^{9}$ rpm), surpassing typical nitrogen-vacancy (NV) center electron spin dephasing rates. Using these NV spins, we observe the effect of the Berry phase arising from particle rotation. In addition, we demonstrate quantum control of spins in a rotating nanodiamond. These results mark an important development in interfacing mechanical rotation with spin qubits, expanding our capacity to study quantum phenomena., Comment: 11+13 pages; 5+8 figures

Accurate electronic structure calculations might be one of the most anticipated applications of quantum computing.The recent landscape of quantum simulations within the Hartree-Fock approximation raises the prospect of substantial theory and hardware developments in this context.Here we propose a general quantum circuit for M{\o}ller-Plesset perturbation theory (MPPT) calculations, which is a popular and powerful post-Hartree-Fock method widly harnessed in solving electronic structure problems. MPPT improves on the Hartree-Fock method by including electron correlation effects wherewith Rayleigh-Schrodinger perturbation theory. Given the Hartree-Fock results, the proposed circuit is designed to estimate the second order energy corrections with MPPT methods. In addition to demonstration of the theoretical scheme, the proposed circuit is further employed to calculate the second order energy correction for the ground state of Helium atom, and the total error rate is around 2.3%. Experiments on IBM 27-qubit quantum computers express the feasibility on near term quantum devices, and the capability to estimate the second order energy correction accurately. In imitation of the classical MPPT, our approach is non-heuristic, guaranteeing that all parameters in the circuit are directly determined by the given Hartree-Fock results. Moreover, the proposed circuit shows a potential quantum speedup comparing to the traditional MPPT calculations. Our work paves the way forward the implementation of more intricate post-Hartree-Fock methods on quantum hardware, enriching the toolkit solving electronic structure problems on quantum computing platforms., Comment: 14 Pages, 4 Figures (in main article)

Alzheimer's disease (AD) is a neurodegenerative disorder that is beginning with amyloidosis, followed by neuronal loss and deterioration in structure, function, and cognition. The accumulation of amyloid-beta in the brain, measured through 18F-florbetapir (AV45) positron emission tomography (PET) imaging, has been widely used for early diagnosis of AD. However, the relationship between amyloid-beta accumulation and AD pathophysiology remains unclear, and causal inference approaches are needed to uncover how amyloid-beta levels can impact AD development. In this paper, we propose a graph varying coefficient neural network (GVCNet) for estimating the individual treatment effect with continuous treatment levels using a graph convolutional neural network. We highlight the potential of causal inference approaches, including GVCNet, for measuring the regional causal connections between amyloid-beta accumulation and AD pathophysiology, which may serve as a robust tool for early diagnosis and tailored care.

The transport properties of matter have been widely investigated. In particular, shear viscosity over a wide parameter space is crucial for various applications, such as designing inertial confinement fusion (ICF) targets and determining the Rayleigh-Taylor instability. In this work, an extended random-walk shielding-potential viscosity model (RWSP-VM) [Phys. Rev. E 106, 014142] based on the statistics of random-walk ions and the Debye shielding effect is proposed to elevate the temperature limit of RWSP-VM in evaluating the shear viscosity of metals. In the extended model, we reconsider the collision diameter that is introduced by hard-sphere concept, hence, it is applicable in both warm and hot temperature regions (10^1-10^7 eV) rather than the warm temperature region (10^1-10^2 eV) in which RWSP-VM is applicable. The results of Be, Al, Fe, and U show that the extended model provides a systematic way to calculate the shear viscosity of arbitrary metals at the densities from about 0.1 to 10 times the normal density (the density at room temperature and 1 standard atmosphere). This work will help to develop viscosity model in wide region when combined with our previous low temperature viscosity model [AIP Adv. 11, 015043]., Comment: 6 pages, 5 figures

Paramagnetic ions and radicals play essential roles in biology and medicine, but detecting these species requires a highly sensitive and ambient-operable sensor. Optically addressable spin color centers in 3D semiconductors have been used for detecting paramagnetic spins as they are sensitive to the spin magnetic noise. However, the distance between spin color centers and target spins is limited due to the difficulty of creating high-quality spin defects near the surface of 3D materials. Here, we show that spin qubits in hexagonal boron nitride (hBN), a layered van der Waals (vdW) material, can serve as a promising sensor for nanoscale detection of paramagnetic spins in liquids. We first create shallow spin defects in close proximity to the hBN surface, which sustain high-contrast optically detected magnetic resonance (ODMR) in liquids. Then we demonstrate sensing spin noise of paramagnetic ions in water based on spin relaxation measurements. Finally, we show that paramagnetic ions can reduce the contrast of spin-dependent fluorescence, enabling efficient detection by continuous wave ODMR. Our results demonstrate the potential of ultrathin hBN quantum sensors for chemical and biological applications., Comment: 4 figures

Color centers in hexagonal boron nitride (hBN) have recently emerged as promising candidates for a new wave of quantum applications. Thanks to hBN's high stability and 2-dimensional (2D) layered structure, color centers in hBN can serve as robust quantum emitters that can be readily integrated into nanophotonic and plasmonic structures on a chip. More importantly, the recently discovered optically addressable spin defects in hBN provide a quantum interface between photons and electron spins for quantum sensing applications. The most well-studied hBN spin defects, the negatively charged boron vacancy ($V_B^-$) spin defects, have been used for quantum sensing of static magnetic fields, magnetic noise, temperature, strain, nuclear spins, paramagnetic spins in liquids, RF signals, and beyond. In particular, hBN nanosheets with spin defects can form van der Waals (vdW) heterostructures with 2D magnetic or other materials for in situ quantum sensing and imaging. This review summarizes the rapidly evolving field of nanoscale and microscale quantum sensing with spin defects in hBN. We introduce basic properties of hBN spin defects, quantum sensing protocols, and recent experimental demonstrations of quantum sensing and imaging with hBN spin defects. We also discuss methods to enhance their sensitivity. Finally, we envision some potential developments and applications of hBN spin defects., Comment: review article, 21 pages, 13 figures

A levitated non-spherical nanoparticle in a vacuum is ideal for studying quantum rotations and is an extremely sensitive torque and force detector. It has been proposed to probe fundamental particle-surface interactions such as the Casimir torque and the rotational quantum vacuum friction, which require it to be driven to rotate near a surface at sub-micrometer separations. Here, we optically levitate a silica nanodumbbell in a vacuum at about 430 nm away from a sapphire surface and drive it to rotate at GHz frequencies. The relative linear speed between the tip of the nanodumbbell and the surface reaches 1.4 km/s at a sub-micrometer separation. The rotating nanodumbbell near the surface demonstrates a torque sensitivity of $(5.0 \pm 1.1) \times 10^{-26} {\rm NmHz}^{-1/2}$ at room temperature. Moreover, we levitate a nanodumbbell near a gold nanograting and use it to probe the near-field intensity distribution beyond the optical diffraction limit. Our numerical simulation shows it is promising to detect the Casimir torque between a nanodumbbell and a nanograting., Comment: 4 figures

Optically active spin defects in van der Waals materials are promising platforms for modern quantum technologies. Here we investigate the coherent dynamics of strongly interacting ensembles of negatively charged boron-vacancy ($\mathrm{V}_{\mathrm{B}}^-$) centers in hexagonal boron nitride (hBN) with varying defect density. By employing advanced dynamical decoupling sequences to selectively isolate different dephasing sources, we observe more than 5-fold improvement in the measured coherence times across all hBN samples. Crucially, we identify that the many-body interaction within the $\mathrm{V}_{\mathrm{B}}^-$ ensemble plays a substantial role in the coherent dynamics, which is then used to directly estimate the concentration of $\mathrm{V}_{\mathrm{B}}^-$. We find that at high ion implantation dosage, only a small portion of the created boron vacancy defects are in the desired negatively charged state. Finally, we investigate the spin response of $\mathrm{V}_{\mathrm{B}}^-$ to the local charged defects induced electric field signals, and estimate its ground state transverse electric field susceptibility. Our results provide new insights on the spin and charge properties of $\mathrm{V}_{\mathrm{B}}^-$, which are important for future use of defects in hBN as quantum sensors and simulators., Comment: 8+8+4 pages, 4+5+1 figures

Two-dimensional hexagonal boron nitride (hBN) has been known to host a variety of quantum emitters with properties suitable for a broad range of quantum photonic applications. Among them, the negatively charged boron vacancy (VB-) defect with optically addressable spin states has emerged recently due to its potential use in quantum sensing. Compared to spin defects in bulk crystals, VB- preserves its spin coherence properties when placed at nanometer-scale distances from the hBN surface, enabling nanometer-scale quantum sensing. On the other hand, the low quantum efficiency of VB- has hindered its use in practical applications. Several studies have reported improving the overall quantum efficiency of VB- defects using plasmonic effects; however, the overall enhancements of up to 17 times reported to date are relatively modest. In this study, we explore and demonstrate much higher emission enhancements of VB- with ultralow-loss nano-patch antenna (NPA) structures. An overall intensity enhancement of up to 250 times is observed for NPA-coupled VB- defects. Since the laser spot exceeds the area of the NPA, where the enhancement occurs, the actual enhancement provided by the NPA is calculated to be ~1685 times, representing a significant increase over the previously reported results. Importantly, the optically detected magnetic resonance (ODMR) contrast is preserved at such exceptionally strong enhancement. Our results not only establish NPA-coupled VB- defects as high-resolution magnetic field sensors operating at weak laser powers, but also provide a promising approach to obtaining single VB- defects., Comment: 17 pages, 4 figures

Vision multi-layer perceptrons (MLPs) have shown promising performance in computer vision tasks, and become the main competitor of CNNs and vision Transformers. They use token-mixing layers to capture cross-token interactions, as opposed to the multi-head self-attention mechanism used by Transformers. However, the heavily parameterized token-mixing layers naturally lack mechanisms to capture local information and multi-granular non-local relations, thus their discriminative power is restrained. To tackle this issue, we propose a new positional spacial gating unit (PoSGU). It exploits the attention formulations used in the classical relative positional encoding (RPE), to efficiently encode the cross-token relations for token mixing. It can successfully reduce the current quadratic parameter complexity $O(N^2)$ of vision MLPs to $O(N)$ and $O(1)$. We experiment with two RPE mechanisms, and further propose a group-wise extension to improve their expressive power with the accomplishment of multi-granular contexts. These then serve as the key building blocks of a new type of vision MLP, referred to as PosMLP. We evaluate the effectiveness of the proposed approach by conducting thorough experiments, demonstrating an improved or comparable performance with reduced parameter complexity. For instance, for a model trained on ImageNet1K, we achieve a performance improvement from 72.14\% to 74.02\% and a learnable parameter reduction from $19.4M$ to $18.2M$. Code could be found at https://github.com/Zhicaiwww/PosMLP.

Force-based algorithms for $\mathit{\text{ab initio}}$ atomic structure relaxation, such as conjugate gradient methods, usually get stuck in the line minimization processes along search directions, where expensive $\mathit{\text{ab initio}}$ calculations are triggered frequently to test trial positions before locating the next iterate. We present a force-based gradient descent method, WANBB, that circumvents the deficiency. At each iteration, WANBB enters the line minimization process with a trial stepsize capturing the local curvature of the energy surface. The exit is controlled by an unrestrictive criterion that tends to accept early trials. These two ingredients streamline the line minimization process in WANBB. The numerical simulations on nearly 80 systems with good universality demonstrate the considerable compression of WANBB on the cost for the unaccepted trials compared with conjugate gradient methods. We also observe across the board significant and universal speedups as well as the superior robustness of WANBB over several widely used methods. The latter point is theoretically established. The implementation of WANBB is pretty simple, in that no a priori physical knowledge is required and only two parameters are present without tuning., Comment: 8 pages, 9 figures

Van der Waals layered materials are a focus of materials research as they support strong quantum effects and can easily form heterostructures. Electron spins in van der Waals materials played crucial roles in many recent breakthroughs, including topological insulators, two-dimensional (2D) magnets, and spin liquids. However, nuclear spins in van der Waals materials remain an unexplored quantum resource. Here we report the first demonstration of optical polarization and coherent control of nuclear spins in a van der Waals material at room temperature. We use negatively-charged boron vacancy ($V_B^-$) spin defects in hexagonal boron nitride to polarize nearby nitrogen nuclear spins. Remarkably, we observe the Rabi frequency of nuclear spins at the excited-state level anti-crossing of $V_B^-$ defects to be 350 times larger than that of an isolated nucleus, and demonstrate fast coherent control of nuclear spins. We also detect strong electron-mediated nuclear-nuclear spin coupling that is 5 orders of magnitude larger than the direct nuclear spin dipolar coupling, enabling multi-qubit operations. Nitrogen nuclear spins in a triangle lattice will be suitable for large-scale quantum simulation. Our work opens a new frontier with nuclear spins in van der Waals materials for quantum information science and technology.

The dynamics of three interacting objects has been investigated extensively in Newtonian gravitational physics (often termed the three-body problem), and is important for many quantum systems, including nuclei, Efimov states, and frustrated spin systems. However, the dynamics of three macroscopic objects interacting through quantum vacuum fluctuations (virtual photons) is still an unexplored frontier. Here, we report the first observation of Casimir interactions between three isolated macroscopic objects. We propose and demonstrate a three terminal switchable architecture exploiting opto-mechanical Casimir interactions that can lay the foundations of a Casimir transistor. Beyond the paradigm of Casimir forces between two objects in different geometries, our Casimir transistor represents an important development for control of three-body virtual photon interactions and will have potential applications in sensing and information processing with the Casimir effect., Comment: 7 pages, 4 figures

Based on ab initio molecular dynamics simulations, we determined the melting curve of magnesium (Mg) up to ~460 GPa using the solid-liquid coexistence method. Between ~30 and 100 GPa, our melting curve is noticeably lower than those from static experiments, but is in good agreement with recent shock experiments. Up to ~450 GPa, our melting curve is generally consistent with the melting points from first-principles calculations using the small-cell coexistence method. We found that, at high pressures of a few hundred GPa, due to the strong softening of interatomic interactions in the liquid phase, solid-liquid coexistence simulations of Mg show some characteristics distinctively different from other metal systems, such as aluminum. For example, at a given volume, the pressure and temperature range for maintaining a stable solid-liquid coexistence state can be very small. The strong softening in the liquid phase also causes the unusual behavior of reentrant melting to occur at very high pressures. The onset of reentrant melting is predicted at ~305 GPa, close to that at ~300 GPa from the small-cell coexistence method. We show that the calculated melting points, considering reentrant melting, can be excellently fitted to a low-order Kechin equation, thereby making it possible for us to obtain a first-principles melting curve of Mg at pressures above 50 GPa for the first time. Similar characteristics in solid-liquid coexistence simulations, as well as reentrant melting, are also expected for other systems with strong softening in the liquid phase at high pressures., Comment: 22 pages, 9 figures

The tactile sensing capabilities of human hands are essential in performing daily activities. Simultaneously perceiving normal and shear forces via the mechanoreceptors integrated into the hands enables humans to achieve daily tasks like grasping delicate objects. In this paper, we design and fabricate a novel biomimetic tactile sensor with skin-like heterogeneity that perceives normal and shear contact forces simultaneously. It mimics the multilayers of mechanoreceptors by combining an extrinsic layer (piezoresistive sensors) and an intrinsic layer (a Hall sensor) so that it can perform estimation of contact force directions, locations, and joint-level torque. By integrating our sensors, a robotic gripper can obtain contact force feedback at fingertips; accordingly, robots can perform challenging tasks, such as tweezers usage, and egg grasping. This insightful sensor design can be customized and applied in different areas of robots and provide them with heterogeneous force sensing, potentially supporting robotics in acquiring skin-like tactile feedback.

Hohenberg-Kohn (HK) theorem is a cornerstone of modern electronic structure calculations. For interacting electrons, given that the internal part of the Hamiltonian ($\hat H_{int}$), containing the kinetic energy and Couloumb interaction of electrons, has a fixed form, the theorem states that when the electrons are subject to an external electrostatic field, the ground-state density can inversely determine the field, and thus the full Hamiltonian completely. For a general quantum system, a HK-type Hamiltonian in the form of $\hat H_{hk}\{g_i\}=\hat H_{int}+\sum_i g_i \hat O_i$ can always be defined, by grouping those terms with fixed or preknown coefficients into $\hat H_{int}$, and factorizing the remaining as superposition of a set of Hermitian operators $\{\hat O_i\}$. We ask whether the HK theorem can be extended, so that the ground-state expectation values of $\{\hat O_i\}$ as the generalized density can in principle be used as the fundamental variables determining all the properties of the system. We show that the question can be addressed by introducing the concept of generalized density correlation matrix (GDCM) defined with respect to the $\{\hat O_i\}$ operators. The invertibility of the GDCM represents a mathematically rigorous and practically useful criterion for the extension of HK theorem to be valid. We apply this criterion to several representative systems, including the quantum Ising dimer, the frustration-free systems, N-level quantum systems with fixed inter-level transition amplitude and tunable level energies, and a fermionic Hubbard chain with inhomogeneous on-site interactions. We suggest that for a finite-size system, finding an invertible GDCM under one single $\{g_i\}$ configuration is typically sufficient to establish the generic extensibility of the HK theorem in the entire parameter space.

The learning objective plays a fundamental role to build a recommender system. Most methods routinely adopt either pointwise or pairwise loss to train the model parameters, while rarely pay attention to softmax loss due to its computational complexity when scaling up to large datasets or intractability for streaming data. The sampled softmax (SSM) loss emerges as an efficient substitute for softmax loss. Its special case, InfoNCE loss, has been widely used in self-supervised learning and exhibited remarkable performance for contrastive learning. Nonetheless, limited recommendation work uses the SSM loss as the learning objective. Worse still, none of them explores its properties thoroughly and answers ``Does SSM loss suit for item recommendation?'' and ``What are the conceptual advantages of SSM loss, as compared with the prevalent losses?'', to the best of our knowledge. In this work, we aim to offer a better understanding of SSM for item recommendation. Specifically, we first theoretically reveal three model-agnostic advantages: (1) mitigating popularity bias; (2) mining hard negative samples; and (3) maximizing the ranking metric. However, based on our empirical studies, we recognize that the default choice of cosine similarity function in SSM limits its ability in learning the magnitudes of representation vectors. As such, the combinations of SSM with the models that also fall short in adjusting magnitudes may result in poor representations. One step further, we provide mathematical proof that message passing schemes in graph convolution networks can adjust representation magnitude according to node degree, which naturally compensates for the shortcoming of SSM. Extensive experiments on four benchmark datasets justify our analyses, demonstrating the superiority of SSM for item recommendation. Our implementations are available in both TensorFlow and PyTorch., Comment: Accepted by TOIS

Discrete time crystals (DTC) have been demonstrated experimentally in several different quantum systems in the past few years. Spin couplings and cavity losses have been shown to play crucial roles for realizing DTC order in open many-body systems out of equilibrium. Recently, it has been proposed that eternal and transient DTC can be present with an open Floquet setup in the thermodynamic limit and in the deep quantum regime with few qubits, respectively. In this work, we consider the effects of spin damping and spin dephasing on the DTC order in spin-optomechanical and open cavity systems in which the spins can be all-to-all coupled. In the thermodynamic limit, it is shown that the existence of dephasing can destroy the coherence of the system and finally lead the system to its trivial steady state. Without dephasing, eternal DTC is displayed in the weak damping regime, which may be destroyed by increasing the all-to-all spin coupling or the spin damping. By contrast, the all-to-all coupling is constructive to the DTC in the moderate damping regime. We also focus on a model which can be experimentally realized by a suspended hexagonal boron nitride (hBN) membrane with a few spin color centers under microwave drive and Floquet magnetic field. Signatures of transient DTC behavior are demonstrated in both weak and moderate dissipation regimes without spin dephasing. Relevant experimental parameters are also discussed for realizing transient DTC order in such an hBN optomechanical system., Comment: 8 pages

The recently discovered spin-active boron vacancy (V$_\text{B}^-$) defect center in hexagonal boron nitride (hBN) has high contrast optically-detected magnetic resonance (ODMR) at room-temperature, with a spin-triplet ground-state that shows promise as a quantum sensor. Here we report temperature-dependent ODMR spectroscopy to probe spin within the orbital excited-state. Our experiments determine the excited-state spin Hamiltonian, including a room-temperature zero-field splitting of 2.1 GHz and a g-factor similar to that of the ground-state. We confirm that the resonance is associated with spin rotation in the excited-state using pulsed ODMR measurements, and we observe Zeeman-mediated level anti-crossings in both the orbital ground- and excited-state. Our observation of a single set of excited-state spin-triplet resonance from 10 to 300 K is consistent with an orbital-singlet, which has consequences for understanding the symmetry of this defect. Additionally, the excited-state ODMR has strong temperature dependence of both contrast and transverse anisotropy splitting, enabling promising avenues for quantum sensing., Comment: 13 pages with 5 figures and a supplement

The multiple scattering theory (MST) is one of the most widely used methods in electronic structure calculations. It features a perfect separation between the atomic configurations and site potentials, and hence provides an efficient way to simulate defected and disordered systems. This work studies the MST methods from a numerical point of view and shows the convergence with respect to the truncation of the angular momentum summations, which is a fundamental approximation parameter for all MST methods. We provide both rigorous analysis and numerical experiments to illustrate the efficiency of the MST methods within the angular momentum representations., Comment: 33 pages, 7 figures

We develop a novel model, called the ``random-walk shielding-potential viscosity model'' (RWSP-VM) that introduces the statistics of random-walk ions and the Debye shielding effect to describe the viscosities of warm dense metals. The viscosities of several metals with low to high atomic number (Be, Al, Fe, and U) are calculated using the analytical expression of RWSP-VM. Additionally, we simulate the viscosities of Fe and Be by employing the Langevin molecular dynamics (MD) and classical MD, while the MD data for Al and U are obtained from a previous work. The results of the RWSP-VM are in good agreement with the MD results, which validates the proposed model. Furthermore, we compare the RWSP-VM with the one-component plasma model and Yukawa viscosity model and show that the three models yield results in excellent agreement with each other in the regime where the RWSP-VM is applicable. These results indicate that the RWSP-VM is a universal, accurate, and highly efficient model for calculating the viscosity of metals in the warm dense state. The code of the proposed RWSP-VM is provided, and it is envisaged that it will have broad application prospects in numerous fields., Comment: 12 pages, 13 figures

We numerically demonstrate that a planar slab made of magnetic Weyl semimetal (a class of topological materials) can emit high-purity circularly polarized (CP) thermal radiation over a broad mid- and long-wave infrared wavelength range for a significant portion of its emission solid angle. This effect fundamentally arises from the strong infrared gyrotropy or nonreciprocity of these materials which primarily depends on the momentum separation between Weyl nodes in the band structure. We clarify the dependence of this effect on the underlying physical parameters and highlight that the spectral bandwidth of CP thermal emission increases with increasing momentum separation between the Weyl nodes. We also demonstrate using recently developed thermal discrete dipole approximation (TDDA) computational method that finite-size bodies of magnetic Weyl semimetals can emit spectrally broadband CP thermal light, albeit over smaller portion of the emission solid angle compared to the planar slabs. Our work identifies unique fundamental and technological prospects of magnetic Weyl semimetals for engineering thermal radiation and designing efficient CP light sources., Comment: 12 pages, 4 figures

The recently discovered spin defects in hexagonal boron nitride (hBN), a layered van der Waals material, have great potential in quantum sensing. However, the photoluminescence and the contrast of the optically detected magnetic resonance (ODMR) of hBN spin defects are relatively low so far, which limits their sensitivity. Here we report a record-high ODMR contrast of 46$\%$ at room temperature, and simultaneous enhancement of the photoluminescence of hBN spin defects by up to 17-fold by the surface plasmon of a gold-film microwave waveguide. Our results are obtained with shallow boron vacancy spin defects in hBN nanosheets created by low-energy He$^+$ ion implantation, and a gold-film microwave waveguide fabricated by photolithography. We also explore the effects of microwave and laser powers on the ODMR, and improve the sensitivity of hBN spin defects for magnetic field detection. Our results support the promising potential of hBN spin defects for nanoscale quantum sensing.

A fundamental prediction of quantum mechanics is that there are random fluctuations everywhere in a vacuum because of the zero-point energy. Remarkably, quantum electromagnetic fluctuations can induce a measurable force between neutral objects, known as the Casimir effect, which has attracted broad interests. The Casimir effect can dominate the interaction between microstructures at small separations and has been utilized to realize nonlinear oscillation, quantum trapping, phonon transfer, and dissipation dilution. However, a non-reciprocal device based on quantum vacuum fluctuations remains an unexplored frontier. Here we report quantum vacuum mediated non-reciprocal energy transfer between two micromechanical oscillators. We modulate the Casimir interaction parametrically to realize strong coupling between two oscillators with different resonant frequencies. We engineer the system's spectrum to have an exceptional point in the parameter space and observe the asymmetric topological structure near it. By dynamically changing the parameters near the exceptional point and utilizing the non-adiabaticity of the process, we achieve non-reciprocal energy transfer with high contrast. Our work represents an important development in utilizing quantum vacuum fluctuations to regulate energy transfer at the nanoscale and build functional Casimir devices.