Band structure is a cornerstone to understand electronic properties of materials. Accurate band structure calculations using a high-level quantum-chemistry theory can be computationally very expensive. It is promising to speed up such calculations wi
th a quantum computer. In this study, we present a quantum algorithm for band structure calculation based on the equation-of-motion (EOM) theory. First, we introduce a new variational quantum eigensolver algorithm named ADAPT-C for ground-state quantum simulation of solids, where the wave function is built adaptively from a complete set of anti-Hermitian operators. Then, on top of the ADAPT-C ground state, quasiparticle energies and the band structure can be calculated using the EOM theory in a quantum-subspace-expansion (QSE) style, where the projected excitation operators guarantee that the killer condition is satisfied. As a proof of principle, such an EOM-ADAPT-C protocol is used to calculate the band structures of silicon and diamond using a quantum computer simulator.
Robotic three-dimensional (3D) ultrasound (US) imaging has been employed to overcome the drawbacks of traditional US examinations, such as high inter-operator variability and lack of repeatability. However, object movement remains a challenge as unex
pected motion decreases the quality of the 3D compounding. Furthermore, attempted adjustment of objects, e.g., adjusting limbs to display the entire limb artery tree, is not allowed for conventional robotic US systems. To address this challenge, we propose a vision-based robotic US system that can monitor the objects motion and automatically update the sweep trajectory to provide 3D compounded images of the target anatomy seamlessly. To achieve these functions, a depth camera is employed to extract the manually planned sweep trajectory after which the normal direction of the object is estimated using the extracted 3D trajectory. Subsequently, to monitor the movement and further compensate for this motion to accurately follow the trajectory, the position of firmly attached passive markers is tracked in real-time. Finally, a step-wise compounding was performed. The experiments on a gel phantom demonstrate that the system can resume a sweep when the object is not stationary during scanning.
In-network computation has been widely used to accelerate data-intensive distributed applications. Some computational tasks, traditional performed on servers, are offloaded to the network (i.e. programmable switches). However, the computational capac
ity of programmable switches is limited to simple integer arithmetic operations while many of applications require on-the-fly floating-point operations. To address this issue, prior approaches either adopt a float-to-integer method or directly offload computational tasks to the local CPUs of switches, incurring accuracy loss and delayed processing. To this end, we propose NetFC, a table-lookup method to achieve on-the-fly in-network floating-point arithmetic operations nearly without accuracy loss. NetFC adopts a divide-and-conquer mechanism that converts the original huge table into several much small tables together with some integer operations. NetFC adopts a scaling-factor mechanism for computational accuracy improvement, and a prefix-based lossless table compression method to reduce the memory overhead. We use different types of datasets to evaluate NetFC. The experimental results show that the average accuracy of NetFC can be as high as up to 99.94% at worst with only 448KB memory consumption. Furthermore, we integrate NetFC into Sonata for detecting Slowloris attack, yielding significant decrease of detection delay.
Given an optimization problem, the Hessian matrix and its eigenspectrum can be used in many ways, ranging from designing more efficient second-order algorithms to performing model analysis and regression diagnostics. When nonlinear models and non-con
vex problems are considered, strong simplifying assumptions are often made to make Hessian spectral analysis more tractable. This leads to the question of how relevant the conclusions of such analyses are for more realistic nonlinear models. In this paper, we exploit deterministic equivalent techniques from random matrix theory to make a emph{precise} characterization of the Hessian eigenspectra for a broad family of nonlinear models, including models that generalize the classical generalized linear models, without relying on strong simplifying assumptions used previously. We show that, depending on the data properties, the nonlinear response model, and the loss function, the Hessian can have emph{qualitatively} different spectral behaviors: of bounded or unbounded support, with single- or multi-bulk, and with isolated eigenvalues on the left- or right-hand side of the bulk. By focusing on such a simple but nontrivial nonlinear model, our analysis takes a step forward to unveil the theoretical origin of many visually striking features observed in more complex machine learning models.
Massive MIMO wireless FDD systems are often confronted by the challenge to efficiently obtain downlink channel state information (CSI). Previous works have demonstrated the potential in CSI encoding and recovery by take advantage of uplink/downlink r
eciprocity between their CSI magnitudes. However, such a framework separately encodes CSI phase and magnitude. To improve CSI encoding, we propose a learning-based framework based on limited CSI feedback and magnitude-aided information. Moving beyond previous works, our proposed framework with a modified loss function enables end-to-end learning to jointly optimize the CSI magnitude and phase recovery performance. Simulations show that the framework outperforms alternate approaches for phase recovery over overall CSI recovery in indoor and outdoor scenarios.
Time series classification problems exist in many fields and have been explored for a couple of decades. However, they still remain challenging, and their solutions need to be further improved for real-world applications in terms of both accuracy and
efficiency. In this paper, we propose a hybrid neural architecture, called Self-Attentive Recurrent Convolutional Networks (SARCoN), to learn multi-faceted representations for univariate time series. SARCoN is the synthesis of long short-term memory networks with self-attentive mechanisms and Fully Convolutional Networks, which work in parallel to learn the representations of univariate time series from different perspectives. The component modules of the proposed architecture are trained jointly in an end-to-end manner and they classify the input time series in a cooperative way. Due to its domain-agnostic nature, SARCoN is able to generalize a diversity of domain tasks. Our experimental results show that, compared to the state-of-the-art approaches for time series classification, the proposed architecture can achieve remarkable improvements for a set of univariate time series benchmarks from the UCR repository. Moreover, the self-attention and the global average pooling in the proposed architecture enable visible interpretability by facilitating the identification of the contribution regions of the original time series. An overall analysis confirms that multi-faceted representations of time series aid in capturing deep temporal corrections within complex time series, which is essential for the improvement of time series classification performance. Our work provides a novel angle that deepens the understanding of time series classification, qualifying our proposed model as an ideal choice for real-world applications.
Recently, an adaptive variational algorithm termed Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver (ADAPT-VQE) has been proposed by Grimsley et al. (Nat. Commun. 10, 3007) while the number of measurements required
to perform this algorithm scales O(N^8). In this work, we present an efficient adaptive variational quantum solver of the Schrodinger equation based on ADAPT-VQE together with the reduced density matrix reconstruction approach, which reduces the number of measurements from O(N^8) to O(N^4). This new algorithm is quite suitable for quantum simulations of chemical systems on near-term noisy intermediate-scale hardware due to low circuit complexity and reduced measurement. Numerical benchmark calculations for small molecules demonstrate that this new algorithm provides an accurate description of the ground-state potential energy curves. In addition, we generalize this new algorithm for excited states with the variational quantum deflation approach and achieve the same accuracy as ground-state simulations.
Ultrasound (US) imaging is widely employed for diagnosis and staging of peripheral vascular diseases (PVD), mainly due to its high availability and the fact it does not emit radiation. However, high inter-operator variability and a lack of repeatabil
ity of US image acquisition hinder the implementation of extensive screening programs. To address this challenge, we propose an end-to-end workflow for automatic robotic US screening of tubular structures using only the real-time US imaging feedback. We first train a U-Net for real-time segmentation of the vascular structure from cross-sectional US images. Then, we represent the detected vascular structure as a 3D point cloud and use it to estimate the longitudinal axis of the target tubular structure and its mean radius by solving a constrained non-linear optimization problem. Iterating the previous processes, the US probe is automatically aligned to the orientation normal to the target tubular tissue and adjusted online to center the tracked tissue based on the spatial calibration. The real-time segmentation result is evaluated both on a phantom and in-vivo on brachial arteries of volunteers. In addition, the whole process is validated both in simulation and physical phantoms. The mean absolute radius error and orientation error ($pm$ SD) in the simulation are $1.16pm0.1~mm$ and $2.7pm3.3^{circ}$, respectively. On a gel phantom, these errors are $1.95pm2.02~mm$ and $3.3pm2.4^{circ}$. This shows that the method is able to automatically screen tubular tissues with an optimal probe orientation (i.e. normal to the vessel) and at the same to accurately estimate the mean radius, both in real-time.
In this paper, we provide a precise characterization of generalization properties of high dimensional kernel ridge regression across the under- and over-parameterized regimes, depending on whether the number of training data n exceeds the feature dim
ension d. By establishing a bias-variance decomposition of the expected excess risk, we show that, while the bias is (almost) independent of d and monotonically decreases with n, the variance depends on n, d and can be unimodal or monotonically decreasing under different regularization schemes. Our refined analysis goes beyond the double descent theory by showing that, depending on the data eigen-profile and the level of regularization, the kernel regression risk curve can be a double-descent-like, bell-shaped, or monotonic function of n. Experiments on synthetic and real data are conducted to support our theoretical findings.
Given a large data matrix, sparsifying, quantizing, and/or performing other entry-wise nonlinear operations can have numerous benefits, ranging from speeding up iterative algorithms for core numerical linear algebra problems to providing nonlinear fi
lters to design state-of-the-art neural network models. Here, we exploit tools from random matrix theory to make precise statements about how the eigenspectrum of a matrix changes under such nonlinear transformations. In particular, we show that very little change occurs in the informative eigenstructure even under drastic sparsification/quantization, and consequently that very little downstream performance loss occurs with very aggressively sparsified or quantized spectral clustering. We illustrate how these results depend on the nonlinearity, we characterize a phase transition beyond which spectral clustering becomes possible, and we show when such nonlinear transformations can introduce spurious non-informative eigenvectors.
