Given the Hamiltonian, the evaluation of unitary operators has been at the heart of many quantum algorithms. Motivated by existing deterministic and random methods, we present a hybrid approach, where Hamiltonians with large amplitude are evaluated a
t each time step, while the remaining terms are evaluated at random. The bound for the mean square error is obtained, together with a concentration bound. The mean square error consists of a variance term and a bias term, arising respectively from the random sampling of the Hamiltonian terms and the operator splitting error. Leveraging on the bias/variance trade-off, the error can be minimized by balancing the two. The concentration bound provides an estimate on the number of gates. The estimates are verified by using numerical experiments on classical computers.
Simultaneous localization and mapping (SLAM) during communication is emerging. This technology promises to provide information on propagation environments and transceivers location, thus creating several new services and applications for the Internet
of Things and environment-aware communication. Using crowdsourcing data collected by multiple agents appears to be much potential for enhancing SLAM performance. However, the measurement uncertainties in practice and biased estimations from multiple agents may result in serious errors. This study develops a robust SLAM method with measurement plug-and-play and crowdsourcing mechanisms to address the above problems. First, we divide measurements into different categories according to their unknown biases and realize a measurement plug-and-play mechanism by extending the classic belief propagation (BP)-based SLAM method. The proposed mechanism can obtain the time-varying agent location, radio features, and corresponding measurement biases (such as clock bias, orientation bias, and received signal strength model parameters), with high accuracy and robustness in challenging scenarios without any prior information on anchors and agents. Next, we establish a probabilistic crowdsourcing-based SLAM mechanism, in which multiple agents cooperate to construct and refine the radio map in a decentralized manner. Our study presents the first BP-based crowdsourcing that resolves the double count and data reliability problems through the flexible application of probabilistic data association methods. Numerical results reveal that the crowdsourcing mechanism can further improve the accuracy of the mapping result, which, in turn, ensures the decimeter-level localization accuracy of each agent in a challenging propagation environment.
We present stochastic consensus and convergence of the discrete consensus-based optimization (CBO) algorithm with random batch interactions and heterogeneous external noises. Despite the wide applications and successful performance in many practical
simulations, the convergence of the discrete CBO algorithm was not rigorously investigated in such a generality. In this work, we introduce a generalized discrete CBO algorithm with a weighted representative point and random batch interactions, and show that the proposed discrete CBO algorithm exhibits stochastic consensus and convergence toward the common equilibrium state exponentially fast under suitable assumptions on system parameters. For this, we recast the given CBO algorithm with random batch interactions as a discrete consensus model with a random switching network topology, and then we use the mixing property of interactions over sufficiently long time interval to derive stochastic consensus and convergence estimates in mean square and almost sure senses. Our proposed analysis significantly improves earlier works on the convergence analysis of CBO models with full batch interactions and homogeneous external noises.
Recently, semantic communication has been brought to the forefront because of its great success in deep learning (DL), especially Transformer. Even if semantic communication has been successfully applied in the sentence transmission to reduce semanti
c errors, existing architecture is usually fixed in the codeword length and is inefficient and inflexible for the varying sentence length. In this paper, we exploit hybrid automatic repeat request (HARQ) to reduce semantic transmission error further. We first combine semantic coding (SC) with Reed Solomon (RS) channel coding and HARQ, called SC-RS-HARQ, which exploits the superiority of the SC and the reliability of the conventional methods successfully. Although the SC-RS-HARQ is easily applied in the existing HARQ systems, we also develop an end-to-end architecture, called SCHARQ, to pursue the performance further. Numerical results demonstrate that SCHARQ significantly reduces the required number of bits for sentence semantic transmission and sentence error rate. Finally, we attempt to replace error detection from cyclic redundancy check to a similarity detection network called Sim32 to allow the receiver to reserve the wrong sentences with similar semantic information and to save transmission resources.
We review the Random Batch Methods (RBM) for interacting particle systems consisting of $N$-particles, with $N$ being large. The computational cost of such systems is of $O(N^2)$, which is prohibitively expensive. The RBM methods use small but random
batches so the computational cost is reduced, per time step, to $O(N)$. In this article we discuss these methods for both classical and quantum systems, the corresponding theory, and applications from molecular dynamics, statistical samplings, to agent-based models for collective behavior, and quantum Monte-Carlo methods.
This study considers the joint location and velocity estimation of UE and scatterers in a three-dimensional mmWave CRAN architecture. Several existing works have achieved satisfactory results with neural networks (NNs) for localization. However, the
black box NN localization method has limited performance and relies on a prohibitive amount of training data. Thus, we propose a model-based learning network for localization by combining NNs with geometric models. Specifically, we first develop an unbiased WLS estimator by utilizing hybrid delay/angular measurements, which determine the location and velocity of the UE in only one estimator, and can obtain the location and velocity of scatterers further. The proposed estimator can achieve the CRLB and outperforms state-of-the-art methods. Second, we establish a NN-assisted localization method (NN-WLS) by replacing the linear approximations in the proposed WLS localization model with NNs to learn higher-order error components, thereby enhancing the performance of the estimator. The solution possesses the powerful learning ability of the NN and the robustness of the proposed geometric model. Moreover, the ensemble learning is applied to improve the localization accuracy further. Comprehensive simulations show that the proposed NN-WLS is superior to the benchmark methods in terms of localization accuracy, robustness, and required time resources.
The radiation magnetohydrodynamics (RMHD) system couples the ideal magnetohydrodynamics equations with a gray radiation transfer equation. The main challenge is that the radiation travels at the speed of light while the magnetohydrodynamics changes w
ith the time scale of the fluid. The time scales of these two processes can vary dramatically. In order to use mesh sizes and time steps that are independent of the speed of light, asymptotic preserving (AP) schemes in both space and time are desired. In this paper, we develop an AP scheme in both space and time for the RMHD system. Two different scalings are considered. One results in an equilibrium diffusion limit system, while the other results in a non-equilibrium system. The main idea is to decompose the radiative intensity into three parts, each part is treated differently with suitable combinations of explicit and implicit discretizations guaranteeing the favorable stability conditionand computational efficiency. The performance of the AP method is presented, for both optically thin and thick regions, as well as for the radiative shock problem.
Recently, reconfigurable intelligent surfaces (RISs) have drawn intensive attention to enhance the coverage of millimeter wave (mmWave) communication systems. However, existing works mainly consider the RIS as a whole uniform plane, which may be unre
alistic to be installed on the facade of buildings when the RIS is extreme large. To address this problem, in this paper, we propose a sparse array of sub-surface (SAoS) architecture for RIS, which contains several rectangle shaped sub-surfaces termed as RIS tiles that can be sparsely deployed. An approximated ergodic spectral efficiency of the SAoS aided system is derived and the performance impact of the SAoS design is evaluated. Based on the approximated ergodic spectral efficiency, we obtain an optimal reflection coefficient design for each RIS tile. Analytical results show that the received signal-to-noise ratios can grow quadratically and linearly to the number of RIS elements under strong and weak LoS scenarios, respectively. Furthermore, we consider the visible region (VR) phenomenon in the SAoS aided mmWave system and find that the optimal distance between RIS tiles is supposed to yield a total SAoS VR nearly covering the whole blind coverage area. The numerical results verify the tightness of the approximated ergodic spectral efficiency and demonstrate the great system performance.
We investigate several important issues regarding the Random Batch Method (RBM) for second order interacting particle systems. We first show the uniform-in-time strong convergence for second order systems under suitable contraction conditions. Second
ly, we propose the application of RBM for singular interaction kernels via kernel splitting strategy, and investigate numerically the application to molecular dynamics.
Sparse signal recovery problems from noisy linear measurements appear in many areas of wireless communications. In recent years, deep learning (DL) based approaches have attracted interests of researchers to solve the sparse linear inverse problem by
unfolding iterative algorithms as neural networks. Typically, research concerning DL assume a fixed number of network layers. However, it ignores a key character in traditional iterative algorithms, where the number of iterations required for convergence changes with varying sparsity levels. By investigating on the projected gradient descent, we unveil the drawbacks of the existing DL methods with fixed depth. Then we propose an end-to-end trainable DL architecture, which involves an extra halting score at each layer. Therefore, the proposed method learns how many layers to execute to emit an output, and the network depth is dynamically adjusted for each task in the inference phase. We conduct experiments using both synthetic data and applications including random access in massive MTC and massive MIMO channel estimation, and the results demonstrate the improved efficiency for the proposed approach.
