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Codesign, an integral part of computer architecture referring to the information interaction in hardware-software stack, is able to boost the algorithm mapping and execution in the computer hardware. This well applies to the noisy intermediate-scale quantum era, where quantum algorithms and quantum processors both need to be shaped to allow for advantages in experimental implementations. The state-of-the-art quantum adiabatic optimization algorithm faces challenges for scaling up, where the deteriorating optimization performance is not necessarily alleviated by increasing the circuit depth given the noise in the hardware. The counterdiabatic term can be introduced to accelerate the convergence, but decomposing the unitary operator corresponding to the counterdiabatic terms into one and two-qubit gates may add additional burden to the digital circuit depth. In this work, we focus on the counterdiabatic protocol with a codesigned approach to implement this algorithm on a photonic quantum processor. The tunable Mach-Zehnder interferometer mesh provides rich programmable parameters for local and global manipulation, making it able to perform arbitrary unitary evolutions. Accordingly, we directly implement the unitary operation associated to the counterdiabatic quantum optimization on our processor without prior digitization. Furthermore, we develop and implement an optimized counterdiabatic method by tackling the higher-order many-body interaction terms. Moreover, we benchmark the performance in the case of factorization, by comparing the final success probability and the convergence speed. In conclusion, we experimentally demonstrate the advantages of a codesigned mapping of counterdiabatic quantum dynamics for quantum computing on photonic platforms., Comment: 9 pages, 4 figures. Comments are welcome

Modern data compression methods are slowly reaching their limits after 80 years of research, millions of papers, and wide range of applications. Yet, the extravagant 6G communication speed requirement raises a major open question for revolutionary new ideas of data compression. We have previously shown all understanding or learning are compression, under reasonable assumptions. Large language models (LLMs) understand data better than ever before. Can they help us to compress data? The LLMs may be seen to approximate the uncomputable Solomonoff induction. Therefore, under this new uncomputable paradigm, we present LMCompress. LMCompress shatters all previous lossless compression algorithms, doubling the lossless compression ratios of JPEG-XL for images, FLAC for audios, and H.264 for videos, and quadrupling the compression ratio of bz2 for texts. The better a large model understands the data, the better LMCompress compresses.

Confocal microscopy, a critical advancement in optical imaging, is widely applied because of its excellent anti-noise ability. However, it has low imaging efficiency and can cause phototoxicity. Optical-sectioning structured illumination microscopy (OS-SIM) can overcome the limitations of confocal microscopy but still face challenges in imaging depth and signal-to-noise ratio (SNR). We introduce the concept of confocal imaging into OS-SIM and propose confocal structured illumination microscopy (CSIM) to enhance the imaging performance of OS-SIM. CSIM exploits the principle of dual photography to reconstruct a dual image from each pixel of the camera. The reconstructed dual image is equivalent to the image obtained by using the spatial light modulator (SLM) as a virtual camera, enabling the separation of the conjugate and non-conjugate signals recorded by the camera pixel. We can reject the non-conjugate signals by extracting the conjugate signal from each dual image to reconstruct a confocal image when establishing the conjugate relationship between the camera and the SLM. We have constructed the theoretical framework of CSIM. Optical-sectioning experimental results demonstrate that CSIM can reconstruct images with superior SNR and greater imaging depth compared with existing OS-SIM. CSIM is expected to expand the application scope of OS-SIM.

We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger (SSH) model with long-range hopping terms. By computing the quantum geometry tensor, we derive exactly expressions for the quantum metric and Berry curvature of the energy band electrons, and we obtain the phase diagram of the model marked by the first Chern number. Furthermore, we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. However, some regions where the Berry curvature is identically zero in the first Brillouin zone results in the degeneracy of the quantum metric, which leads to ill-defined non-integer topological Euler numbers. Nevertheless, the non-integer "Euler number" provides valuable insights and provide an upper bound for absolute values of the Chern numbers., Comment: 6 pages, 4 figures

The Multi-Agent Path Finding (MAPF) problem entails finding collision-free paths for a set of agents, guiding them from their start to goal locations. However, MAPF does not account for several practical task-related constraints. For example, agents may need to perform actions at goal locations with specific execution times, adhering to predetermined orders and timeframes. Moreover, goal assignments may not be predefined for agents, and the optimization objective may lack an explicit definition. To incorporate task assignment, path planning, and a user-defined objective into a coherent framework, this paper examines the Task Assignment and Path Finding with Precedence and Temporal Constraints (TAPF-PTC) problem. We augment Conflict-Based Search (CBS) to simultaneously generate task assignments and collision-free paths that adhere to precedence and temporal constraints, maximizing an objective quantified by the return from a user-defined reward function in reinforcement learning (RL). Experimentally, we demonstrate that our algorithm, CBS-TA-PTC, can solve highly challenging bomb-defusing tasks with precedence and temporal constraints efficiently relative to MARL and adapted Target Assignment and Path Finding (TAPF) methods.

Building general-purpose robots that can operate seamlessly, in any environment, with any object, and utilizing various skills to complete diverse tasks has been a long-standing goal in Artificial Intelligence. Unfortunately, however, most existing robotic systems have been constrained - having been designed for specific tasks, trained on specific datasets, and deployed within specific environments. These systems usually require extensively-labeled data, rely on task-specific models, have numerous generalization issues when deployed in real-world scenarios, and struggle to remain robust to distribution shifts. Motivated by the impressive open-set performance and content generation capabilities of web-scale, large-capacity pre-trained models (i.e., foundation models) in research fields such as Natural Language Processing (NLP) and Computer Vision (CV), we devote this survey to exploring (i) how these existing foundation models from NLP and CV can be applied to the field of robotics, and also exploring (ii) what a robotics-specific foundation model would look like. We begin by providing an overview of what constitutes a conventional robotic system and the fundamental barriers to making it universally applicable. Next, we establish a taxonomy to discuss current work exploring ways to leverage existing foundation models for robotics and develop ones catered to robotics. Finally, we discuss key challenges and promising future directions in using foundation models for enabling general-purpose robotic systems. We encourage readers to view our living GitHub repository of resources, including papers reviewed in this survey as well as related projects and repositories for developing foundation models for robotics.

While Large Language Models (LLMs) have demonstrated impressive accomplishments in both reasoning and planning, their abilities in multi-agent collaborations remains largely unexplored. This study evaluates LLM-based agents in a multi-agent cooperative text game with Theory of Mind (ToM) inference tasks, comparing their performance with Multi-Agent Reinforcement Learning (MARL) and planning-based baselines. We observed evidence of emergent collaborative behaviors and high-order Theory of Mind capabilities among LLM-based agents. Our results reveal limitations in LLM-based agents' planning optimization due to systematic failures in managing long-horizon contexts and hallucination about the task state. We explore the use of explicit belief state representations to mitigate these issues, finding that it enhances task performance and the accuracy of ToM inferences for LLM-based agents., Comment: Accepted to EMNLP 2023 (Main Conference). Code available at https://github.com/romanlee6/multi_LLM_comm

We propose atomtronic counterpart of superconducting quantum interference device (SQUID) in synthetic $2$-dimensional space. The system is composed of Bose-Einstein condensate (BEC) in two neighboring optical wells which is coupled to an external coherent light. Furthermore, availability of controllable atomtronic flux qubit in the synthetic dimensions is demonstrated with this system. Control parameter for the qubit is naturally provided by artificial magnetic flux originated from the coherent atom-light coupling. Comparing with traditional SQUID which requires at least $2$-dimensional circuits, the synthetic dimensional SQUID can be realized only in $1$-dimensional circuits. It should be a great advantage for the scalability and integration feature of quantum logic gates., Comment: 8 pages, 3 figures

Mobile communication standards were developed for enhancing transmission and network performance by using more radio resources and improving spectrum and energy efficiency. How to effectively address diverse user requirements and guarantee everyone's Quality of Experience (QoE) remains an open problem. The Sixth Generation (6G) mobile systems will solve this problem by utilizing heterogenous network resources and pervasive intelligence to support everyone-centric customized services anywhere and anytime. In this article, we first coin the concept of Service Requirement Zone (SRZ) on the user side to characterize and visualize the integrated service requirements and preferences of specific tasks of individual users. On the system side, we further introduce the concept of User Satisfaction Ratio (USR) to evaluate the system's overall service ability of satisfying a variety of tasks with different SRZs. Then, we propose a network Artificial Intelligence (AI) architecture with integrated network resources and pervasive AI capabilities for supporting customized services with guaranteed QoEs. Finally, extensive simulations show that the proposed network AI architecture can consistently offer a higher USR performance than the cloud AI and edge AI architectures with respect to different task scheduling algorithms, random service requirements, and dynamic network conditions., Comment: The current version has partial Insufficient completion, so we would like to withdraw it. We hope you agree, thank you

A tensor nuclear norm (TNN) based method for solving the tensor recovery problem was recently proposed, and it has achieved state-of-the-art performance. However, it may fail to produce a highly accurate solution since it tends to treats each frontal slice and each rank component of each frontal slice equally. In order to get a recovery with high accuracy, we propose a general and flexible rank relaxation function named double weighted nonconvex nonsmooth rank (DWNNR) relaxation function for efficiently solving the third order tensor recovery problem. The DWNNR relaxation function can be derived from the triple nonconvex nonsmooth rank (TNNR) relaxation function by setting the weight vector to be the hypergradient value of some concave function, thereby adaptively selecting the weight vector. To accelerate the proposed model, we develop the general inertial smoothing proximal gradient method. Furthermore, we prove that any limit point of the generated subsequence is a critical point. Combining the Kurdyka-Lojasiewicz (KL) property with some milder assumptions, we further give its global convergence guarantee. Experimental results on a practical tensor completion problem with both synthetic and real data, the results of which demonstrate the efficiency and superior performance of the proposed algorithm.

Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency. To this end, we first establish the relationship between matrix rank and tensor tubal rank, and then reformulate matrix completion problem as a tensor completion problem. For the reformulated tensor completion problem, we adopt a two-stage strategy based on tensor factorization algorithm. In this way, a matrix completion problem of big size can be solved via some matrix computations of smaller sizes. For a third order tensor completion problem, to fully exploit the low rank structures, we introduce the double tubal rank which combines the tubal rank and the rank of the mode-3 unfolding matrix. For the mode-3 unfolding matrix rank, we follow the idea of matrix completion. Based on this, we establish a novel model and modify the tensor factorization based algorithm for third order tensor completion. Extensive numerical experiments demonstrate that the proposed methods outperform state-of-the-art methods in terms of both accuracy and running time.

Photovoltaic effect of neutral atoms using inhomogeneous light in double-trap opened system is studied theoretically. Using asymmetric external driving field to replacing original asymmetric chemical potential of atoms, we create polarization of atom population in the double-trap system. The polarization of atom number distribution induces net current of atoms and works as collected carriers in the cell. The cell can work even under partially coherent light. The whole configuration is described by quantum master equation considering weak tunneling between the system and its reservoirs at finite temperature. The model of neutral atoms could be extended to more general quantum particles in principle., Comment: 8 pages, 4 figures

In this paper, we study the low-rank matrix minimization problem, where the loss function is convex but nonsmooth and the penalty term is defined by the cardinality function. We first introduce an exact continuous relaxation, that is, both problems have the same minimzers and the same optimal value. In particular, we introduce a class of lifted stationary point of the relaxed problem and show that any local minimizer of the relaxed problem must be a lifted stationary point. In addition, we derive lower bound property for the nonzero singular values of the lifted stationary point and hence also of the local minimizers of the relaxed problem. Then the smoothing proximal gradient (SPG) algorithm is proposed to find a lifted stationary point of the continuous relaxation model. Moreover, it is shown that the whole sequence generated by SPG algorithm converges to a lifted stationary point. At last, numerical examples show the efficiency of the SPG algorithm., Comment: 19 pages

Recently, a tensor factorization based method for a low tubal rank tensor completion problem of a third order tensor was proposed, which performed better than some existing methods. Tubal rank is only defined on one mode of third order tensor without low rank structure in the other two modes. That is, low rank structures on the other two modes are missing. Motivated by this, we first introduce multi-tubal rank, and then establish a relationship between multi-tubal rank and Tucker rank. Based on the multi-tubal rank, we propose a novel low rank tensor completion model. For this model, a tensor factorization based method is applied and the corresponding convergence anlysis is established. In addition, spatio-temporal characteristics are intrinsic features in video and internet traffic tensor data. To get better performance, we make full use of such features and improve the established tensor completion model. Then we apply tensor factorization based method for the improved model. Finally, numerical results are reported on the completion of image, video and internet traffic data to show the efficiency of our proposed methods. From the reported numerical results, we can assert that our methods outperform the existing methods.

Nowadays consumer loan plays an important role in promoting the economic growth, and credit cards are the most popular consumer loan. One of the most essential parts in credit cards is the credit limit management. Traditionally, credit limits are adjusted based on limited heuristic strategies, which are developed by experienced professionals. In this paper, we present a data-driven approach to manage the credit limit intelligently. Firstly, a conditional independence testing is conducted to acquire the data for building models. Based on these testing data, a response model is then built to measure the heterogeneous treatment effect of increasing credit limits (i.e. treatments) for different customers, who are depicted by several control variables (i.e. features). In order to incorporate the diminishing marginal effect, a carefully selected log transformation is introduced to the treatment variable. Moreover, the model's capability can be further enhanced by applying a non-linear transformation on features via GBDT encoding. Finally, a well-designed metric is proposed to properly measure the performances of compared methods. The experimental results demonstrate the effectiveness of the proposed approach., Comment: 7 pages

The economic and banking importance of the small and medium enterprise (SME) sector is well recognized in contemporary society. Business credit loans are very important for the operation of SMEs, and the revenue is a key indicator of credit limit management. Therefore, it is very beneficial to construct a reliable revenue forecasting model. If the uncertainty of an enterprise's revenue forecasting can be estimated, a more proper credit limit can be granted. Natural gradient boosting approach, which estimates the uncertainty of prediction by a multi-parameter boosting algorithm based on the natural gradient. However, its original implementation is not easy to scale into big data scenarios, and computationally expensive compared to state-of-the-art tree-based models (such as XGBoost). In this paper, we propose a Scalable Natural Gradient Boosting Machines that is simple to implement, readily parallelizable, interpretable and yields high-quality predictive uncertainty estimates. According to the characteristics of revenue distribution, we derive an uncertainty quantification function. We demonstrate that our method can distinguish between samples that are accurate and inaccurate on revenue forecasting of SMEs. What's more, interpretability can be naturally obtained from the model, satisfying the financial needs.

Ant Credit Pay is a consumer credit service in Ant Financial Service Group. Similar to credit card, loan default is one of the major risks of this credit product. Hence, effective algorithm for default prediction is the key to losses reduction and profits increment for the company. However, the challenges facing in our scenario are different from those in conventional credit card service. The first one is scalability. The huge volume of users and their behaviors in Ant Financial requires the ability to process industrial-scale data and perform model training efficiently. The second challenges is the cold-start problem. Different from the manual review for credit card application in conventional banks, the credit limit of Ant Credit Pay is automatically offered to users based on the knowledge learned from big data. However, default prediction for new users is suffered from lack of enough credit behaviors. It requires that the proposal should leverage other new data source to alleviate the cold-start problem. Considering the above challenges and the special scenario in Ant Financial, we try to incorporate default prediction with network information to alleviate the cold-start problem. In this paper, we propose an industrial-scale distributed network representation framework, termed NetDP, for default prediction in Ant Credit Pay. The proposal explores network information generated by various interaction between users, and blends unsupervised and supervised network representation in a unified framework for default prediction problem. Moreover, we present a parameter-server-based distributed implement of our proposal to handle the scalability challenge. Experimental results demonstrate the effectiveness of our proposal, especially in cold-start problem, as well as the efficiency for industrial-scale dataset., Comment: 2018 IEEE International Conference on Big Data (Big Data)

With the rapid growth of financial services, fraud detection has been a very important problem to guarantee a healthy environment for both users and providers. Conventional solutions for fraud detection mainly use some rule-based methods or distract some features manually to perform prediction. However, in financial services, users have rich interactions and they themselves always show multifaceted information. These data form a large multiview network, which is not fully exploited by conventional methods. Additionally, among the network, only very few of the users are labelled, which also poses a great challenge for only utilizing labeled data to achieve a satisfied performance on fraud detection. To address the problem, we expand the labeled data through their social relations to get the unlabeled data and propose a semi-supervised attentive graph neural network, namedSemiGNN to utilize the multi-view labeled and unlabeled data for fraud detection. Moreover, we propose a hierarchical attention mechanism to better correlate different neighbors and different views. Simultaneously, the attention mechanism can make the model interpretable and tell what are the important factors for the fraud and why the users are predicted as fraud. Experimentally, we conduct the prediction task on the users of Alipay, one of the largest third-party online and offline cashless payment platform serving more than 4 hundreds of million users in China. By utilizing the social relations and the user attributes, our method can achieve a better accuracy compared with the state-of-the-art methods on two tasks. Moreover, the interpretable results also give interesting intuitions regarding the tasks., Comment: icdm

The coming 5G networks have been enabling the creation of a wide variety of new services and applications which demand a new network security architecture. Immunology is the study of the immune system in vertebrates (including humans) which protects us from infection through various lines of defence. By studying the resemblance between the immune system and network security system, we acquire some inspirations from immunology and distill some guidelines for the design of network security architecture. We present a philosophical design principle, that is maintaining the balance between security and availability. Then, we derive two methodological principles: 1) achieving situation-awareness and fast response through community cooperation among heterogeneous nodes, and 2) Enhancing defense capability through consistently contesting with invaders in a real environment and actively mutating/evolving attack strategies. We also present a reference architecture designed based on the principles.

The topological Euler characteristic number of the energy band proposed in our previous work (see Yu-Quan Ma et al., arXiv:1202.2397; EPL 103, 10008 (2013)) has been recently experimentally observed by X. Tan et al., Phys. Rev. Lett. \textbf{122}, 210401 (2019), in which a topological phase transition in a time-reversal-symmetric system simulated by the superconducting circuits is witnessed by the Euler number of the occupied band instead of the vanishing Chern number. However, we note that there are some confusions about the non-integer behaviors of the Euler number in the topological trivial phase. In this paper, we show that the reason is straightforward because the quantum metric tensor $g_{\mu \nu} $ is actually positive semi-definite. In a general two-dimensional two-band system, we can proved that: (1) If the phase is topological trivial, then the quantum metric must be degenerate (singular)~--- $\det {g_{\mu \nu} }=0$ in some region of the first Brillouin zone. This leads to the invalidity of the Gauss-Bonnet formula and exhibits an ill-defined ``non-integer Euler number''; (2) If the phase is topological nontrivial with a non-vanishing Berry curvature, then the quantum metric will be a positive definite Riemann metric in the entire first Brillouin zone. Therefore the Euler number of the energy band will be guaranteed an even number $\chi=2(1-g)$ by the Gauss-Bonnet theorem on the closed two-dimensional Bloch energy band manifold with the genus $g$, which provides an effective topological index for a class of nontrivial topological phases., Comment: 5 pages, 4 figures

With fast development of Internet of Everything (IoE) and its applications, the ever increasing mobile internet traffic and services bring unprecedented challenges including scalability, mobility, availability, and security which cannot be addressed by the current clean-slate network architecture. In this paper, a cybertwin based next generation network architecture is proposed to accomodate the evolution from end-to-end connection to cloud-to-end connection in the future network. As a digital representation of human or things in the virtual cyberspace, cybertwin serves in multiple capacities, such as communications assistant, network data logger, and digital asset owner. The new and unique characteristics of the cybertwin make the proposed network to be flexible, scalable, reliable, and secure. Further, we advocate a new cloud network operating system which can work in a distributed way through a real-time multi-agent trading platform to allocate 3C (computing, caching, communications) resources. We also propose cloud operator, a new operator that can provide and manage the resources to the end users and offer location and authentication services for human and things in the cyberspace. Some promising and open research topics are discussed to envision the challenges and opportunities of the cybertwin in the future network architecture., Comment: 14 pages, 5 figures, submitted to IEEE Wireless Communications Magazine on 7 April 2019

In this paper, we introduce a lightweight dynamic epistemic logical framework for automated planning under initial uncertainty. We reduce plan verification and conformant planning to model checking problems of our logic. We show that the model checking problem of the iteration-free fragment is PSPACE-complete. By using two non-standard (but equivalent) semantics, we give novel model checking algorithms to the full language and the iteration-free language., Comment: In Proceedings TARK 2015, arXiv:1606.07295

A Bradbury-Nielsen gate (BNG) is often used to modulate ion beams. It consists of two interleaved and electrically isolated sets of wires with uniform tension, which can keep parallel, equidistant, and coplanar over a wide temperature range, making the BNG reliable and robust. We have previously analyzed the non-uniform problem of wire tensions with sequentially winding method, and developed a template-based transfer method to solve this problem. In this paper, we introduced a progressively reduced pretension method, which allows directly and sequentially winding wires on the substrate without using a template. Theoretical analysis shows that by applying proper pretension to each wire when fixing it onto the substrate, the final wire tensions of all wires can be uniform. The algorithm and flowchart to calculate the pretension sequence are given, and the fabrication process is introduced in detail. Pretensions are generated by weights combination with a homebuilt weaving device. A BNG with stainless steel wire and a printed circuit board substrate is constructed with this method. The non-uniformity of the final wire tensions is less than 2.5% in theory. The BNG is successfully employed in our homemade ion mobility spectrometer, and the measured resolution is 33.5 at a gate opening time of 350 {\mu}s. Compared to the template-based method, this method is simpler, faster and more flexible when making BNGs with different configurations.

This paper presents a flexible irregular model for heterogeneous cloud storage systems and investigates how the cost of repairing failed nodes can be minimized. The fractional repetition code, originally designed for minimizing repair bandwidth for homogeneous storage systems, is generalized to the irregular fractional repetition code, which is adaptable to heterogeneous environments. The code structure and the associated storage allocation can be obtained by solving an integer linear programming problem. For moderate sized networks, a heuristic algorithm is proposed and shown to be near-optimal by computer simulations., Comment: 12 pages, 10 figures. to appear in IEEE Journal on Selected Areas in Communications 2014

We investigate the ground-state Riemannian metric and the cyclic quantum distance of an inhomogeneous quantum Ising spin-1/2 chain in a transverse field. This model can be diagonalized by using a general canonical transformation to the fermionic Hamiltonian mapped from the spin system. The ground-state Riemannian metric is derived exactly on a parameter manifold ring $S^1$, which is introduced by performing a gauge transformation to the spin Hamiltonian through a twist operator. The ground-state cyclic quantum distance and the second derivative of the ground-state energy are studied in different inhomogeneous exchange coupling parameter region. Particularly, we show that the quantum ferromagnetic phase in the uniform Ising chain can be characterized by an invariant cyclic quantum distance with a constant ground-state Riemannian metric, and this metric will rapidly decay to zero in the paramagnetic phase., Comment: 6 pages, 5 figures

We study the Riemannian metric and the Euler characteristic number of the Bloch band in a 1D spin model with multi-site spins exchange interactions. The Euler number of the Bloch band originates from the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. We study this approach analytically in a transverse field XY spin chain with three-site spin coupled interactions. We define a class of cyclic quantum distance on the Bloch band and on the ground state, respectively, as a local characterization for quantum phase transitions. Specifically, we give a general formula for the Euler number by means of the Berry curvature in the case of two-band models, which reveals its essential relation to the first Chern number of the band insulators. Finally, we show that the ferromagnetic-paramagnetic phases transition in zero-temperature can be distinguished by the Euler number of the Bloch band., Comment: 10 pages, 11 figures, some typos are corrected, the published version

The notion of geometric phase has been recently introduced to analyze the quantum phase transitions of many-body systems from the geometrical perspective. In this work, we study the geometric phase of the ground state for an inhomogeneous period-two anisotropic XY model in a transverse field. This model encompasses a group of familiar spin models as its special cases and shows a richer critical behavior. The exact solution is obtained by mapping on a fermionic system through the Jordan-Wigner transformation and constructing the relevant canonical transformation to realize the diagonalization of the Hamiltonian coupled in the $k$-space. The results show that there may exist more than one quantum phase transition point at some parameter regions and these transition points correspond to the divergence or extremum properties of the Berry curvature., Comment: 6 pages, 3 figures. As a backup of a previous work and some typos in the published version are fixed

We propose a topological Euler number to characterize nontrivial topological phases of gapped fermionic systems, which originates from the Gauss-Bonnet theorem on the Riemannian structure of Bloch states established by the real part of the quantum geometric tensor in momentum space. Meanwhile, the imaginary part of the geometric tensor corresponds to the Berry curvature which leads to the Chern number characterization. We discuss the topological numbers induced by the geometric tensor analytically in a general two-band model. As an example, we show that the zero-temperature phase diagram of a transverse field XY spin chain can be distinguished by the Euler characteristic number of the Bloch states manifold in a (1+1)-dimensional Bloch momentum space.

In a distributed storage system, the storage costs of different storage nodes, in general, can be different. How to store a file in a given set of storage nodes so as to minimize the total storage cost is investigated. By analyzing the min-cut constraints of the information flow graph, the feasible region of the storage capacities of the nodes can be determined. The storage cost minimization can then be reduced to a linear programming problem, which can be readily solved. Moreover, the tradeoff between storage cost and repair-bandwidth is established., Comment: 5 pages, 4 figures, to appear in Proc. IEEE GLOBECOM, 2011

We propose a generalized quantum geometric tenor to understand topological quantum phase transitions, which can be defined on the parameter space with the adiabatic evolution of a quantum many-body system. The generalized quantum geometric tenor contains two different local measurements, the non-Abelian Riemannian metric and the non-Abelian Berry curvature, which are recognized as two natural geometric characterizations for the change of the ground-state properties when the parameter of the Hamiltonian varies. Our results show the symmetry-breaking and topological quantum phase transitions can be understood as the singular behavior of the local and topological properties of the quantum geometric tenor in the thermodynamic limit., Comment: 5 pages, 2 figures