Trainability Analysis of Quantum Optimization Algorithms from a Bayesian Lens

The Quantum Approximate Optimization Algorithm (QAOA) is an extensively studied variational quantum algorithm utilized for solving optimization problems on near-term quantum devices. A significant focus is placed on determining the effectiveness of training the $n$-qubit QAOA circuit, i.e., whether the optimization error can converge to a constant level as the number of optimization iterations scales polynomially with the number of qubits. In realistic scenarios, the landscape of the corresponding QAOA objective function is generally non-convex and contains numerous local optima. In this work, motivated by the favorable performance of Bayesian optimization in handling non-convex functions, we theoretically investigate the trainability of the QAOA circuit through the lens of the Bayesian approach. This lens considers the corresponding QAOA objective function as a sample drawn from a specific Gaussian process. Specifically, we focus on two scenarios: the noiseless QAOA circuit and the noisy QAOA circuit subjected to local Pauli channels. Our first result demonstrates that the noiseless QAOA circuit with a depth of $\tilde{\mathcal{O}}\left(\sqrt{\log n}\right)$ can be trained efficiently, based on the widely accepted assumption that either the left or right slice of each block in the circuit forms a local 1-design. Furthermore, we show that if each quantum gate is affected by a $q$-strength local Pauli channel with the noise strength range of $1/{\rm poly} (n)$ to 0.1, the noisy QAOA circuit with a depth of $\mathcal{O}\left(\log n/\log(1/q)\right)$ can also be trained efficiently. Our results offer valuable insights into the theoretical performance of quantum optimization algorithms in the noisy intermediate-scale quantum era

Search for Eccentric Black Hole Coalescences during the Third Observing Run of LIGO and Virgo

Despite the growing number of confident binary black hole coalescences observed through gravitational waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity is one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however, remains challenging due to the limited availability of gravitational waveforms that include effects of eccentricity. Here, we present observational results for a waveform-independent search sensitive to eccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detectors. We identified no new high-significance candidates beyond those that were already identified with searches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass (total mass $M>70$ $M_\odot$) binaries covering eccentricities up to 0.3 at 15 Hz orbital frequency, and use this to compare model predictions to search results. Assuming all detections are indeed quasi-circular, for our fiducial population model, we place an upper limit for the merger rate density of high-mass binaries with eccentricities $0 < e \leq 0.3$ at $0.33$ Gpc$^{-3}$ yr$^{-1}$ at 90\% confidence level.Comment: 24 pages, 5 figure

Search for eccentric black hole coalescences during the third observing run of LIGO and Virgo

Despite the growing number of confident binary black hole coalescences observed through gravitational waves so far, the astrophysical origin of these binaries remains uncertain. Orbital eccentricity is one of the clearest tracers of binary formation channels. Identifying binary eccentricity, however, remains challenging due to the limited availability of gravitational waveforms that include effects of eccentricity. Here, we present observational results for a waveform-independent search sensitive to eccentric black hole coalescences, covering the third observing run (O3) of the LIGO and Virgo detectors. We identified no new high-significance candidates beyond those that were already identified with searches focusing on quasi-circular binaries. We determine the sensitivity of our search to high-mass (total mass M&gt;70 M⊙) binaries covering eccentricities up to 0.3 at 15 Hz orbital frequency, and use this to compare model predictions to search results. Assuming all detections are indeed quasi-circular, for our fiducial population model, we place an upper limit for the merger rate density of high-mass binaries with eccentricities 0&lt;e≤0.3 at 0.33 Gpc−3 yr−1 at 90\% confidence level

Response of Soil Respiration to Altered Snow Cover in a Typical Temperate Grassland in China

The snow cover in temperate areas is undergoing significant changes, which may affect soil respiration (Rs), the second largest carbon flux in global carbon cycling. However, currently, there are relatively few in situ field studies on the effects of altered snow cover on Rs in temperate areas during the non-growing season compared to the research on Rs during the growing season. Therefore, it limited the accurate prediction of the characteristics and magnitude of changes in soil carbon emissions in temperate areas under global change scenarios. Here, an in situ field experiment was conducted in a typical grassland in Inner Mongolia in China to explore the characteristics of Rs under three different snow cover treatments, i.e., increasing snow (IS), decreasing snow (DS), and ambient snow that was regarded as the control check treatment (CK). The results showed that the range of Rs flux and cumulative emission flux in all treatments in the non-growing season in the study area ranged from 5.87 ± 0.20 to 55.11 ± 6.42 mg CO2 m−2 h−1 and from 22.81 ± 0.68 to 26.36 ± 0.41 g C m−2, respectively. During the observation period, the depth of the largest snow cover for each treatment did not exceed 18 cm, and none of the snow treatments caused significant variations in Rs flux (p > 0.05). However, the cumulative flux of Rs in the whole non-growing season was only stimulated significantly by 15.6% by the IS treatment compared with that of CK. The relatively high Rs flux in the non-growing season was observed to mainly occur in the soil deeply frozen period (DFP) and the soil melting period (SMP). Further analysis revealed that Rs flux under different snow treatments were mainly positively correlated with soil temperature during SMP. The main factors controlling Rs varied with different sampling periods. Our findings suggest that the non-growing season is also an important period of non-negligible carbon emissions from typical grassland soils in temperate zones

Blockchain-Based Auditable Privacy-Preserving Data Classification for Internet of Things

Internet of Things (IoT) connects massive physical devices to capture and collect useful data, which are used to make accurate decisions by taking advantage of the machine learning techniques. However, the collected data may contain users' sensitive information. When guaranteeing the utility of data, we need to consider privacy of users' data. To balance the utility and the privacy of data, the existing approaches usually adopt the privacy-preserving signature technology, where the privacy-preserving data are classified by a designated converter (data processor) interacting with a semihonest verifier (data center). However, for the malicious behavior of the data center and data processor, this kind of approach is insufficient. To prevent the malicious data center/data processor while guaranteeing the utility and privacy of data, we propose blockchain-based auditable privacy-preserving data classification (PPDC) scheme for IoT. We put forth a new controllably linkable group signature (CL-GS) to balance the utility and privacy of data and take advantage of blockchain to audit the correctness of privacy-preserving data classification against malicious data processor/data center. We formalize the system model of the auditable privacy-preserving data classification in the blockchain setting and its security model. Then, we present a concrete construction and prove its security in the random oracle model. Finally, we deploy a prototype system to evaluate the performance of PPDC.This work was supported in part by the National Natural Science Foundation of China under Grant 61872229 and Grant U19B2021; in part by the Blockchain Core Technology Strategic Research Program of Ministry of Education of China under Grant 2020KJ010301; and in part by the Key Research and Development Program of Shaanxi under Grant 2021ZDLGY06-04 and Grant 2020ZDLGY09-06

Multi-Scale Characterization of Spatial Variability of Soil Organic Carbon in a Semiarid Zone in Northern China

The variation of soil organic carbon (SOC) spatial distribution is dependent on the relative contributions of different environmental factors, and the dominant factors change according to study scales. Here, geostatistical and remote sensing techniques were used to gain deep knowledge about SOC spatial distribution patterns and their dominant determinants at different study scales; specifically, the structure of the spatial variability of SOC content at the county, regional, and watershed scales in Aohan, China were analyzed. The results show that altitude and normalized difference vegetation index (NDVI) are the key predictors explaining 49.6% of the SOC variability at the county scale; NDVI and slope are the key predictors explaining 36.2% of the SOC variability at the regional scale; and terrain factors are the most significant factors at the watershed scale. These three scales have a moderate spatial correlation in terms of SOC content. As the study scale widens, the spatial variability attributable to the random factors increases gradually, whereas the variability attributable to the structural factors gradually weakens. Soil type and land use type are the key factors influencing the SOC content at these three scales. At all scales, the SOC contents of the different land use types differ significantly in the order forestland > shrubland > grassland. Conservation of regional soil and water and prevention of soil desertification are effective measures for improving SOC content

Three-Dimensional Path-Following Control Method for Flying–Walking Power Line Inspection Robot Based on Improved Line of Sight

The Flying–Walking Power Line Inspection Robot (FPLIR) faces challenges in maintaining stability and reliability when operating in harsh transmission line environments with complex conditions. The robot often switches modes frequently to land accurately on the line, resulting in increasing following errors and premature or delayed switching caused by reference path switching. To address these issues, a path-following control method based on improved line of sight (LOS) is proposed. The method features an adaptive acceptance circle strategy that adjusts the radius of the acceptance circle of the path point based on the angle of the path segment and the flight speed at the time of switching, improving path-following accuracy during reference trajectory switching. Also, an adaptive heading control with vertical distance feedback is designed to prioritize different path-following methods in real time based on variations in vertical distance, achieving rapid convergence along the following path. The state feedback following control law, based on the improved LOS, achieves the stable following of the reference path, which was validated by simulations. The simulation results show that the improved LOS reduces the convergence time by 0.8 s under controllable error conditions for path angles of θ ∈ (0, π⁄2). For path angles of θ ∈ (π⁄2, π), the following error is reduced by 0.3 m, and the convergence time is reduced by 0.4 s. These results validate the feasibility and effectiveness of the proposed method. This method demonstrates advantages over the traditional LOS in terms of following accuracy and convergence speed, providing theoretical references for future 3D path following for path-following robots and aerial vehicles

Multi-Scale Characterization of Spatial Variability of Soil Organic Carbon in a Semiarid Zone in Northern China

The variation of soil organic carbon (SOC) spatial distribution is dependent on the relative contributions of different environmental factors, and the dominant factors change according to study scales. Here, geostatistical and remote sensing techniques were used to gain deep knowledge about SOC spatial distribution patterns and their dominant determinants at different study scales; specifically, the structure of the spatial variability of SOC content at the county, regional, and watershed scales in Aohan, China were analyzed. The results show that altitude and normalized difference vegetation index (NDVI) are the key predictors explaining 49.6% of the SOC variability at the county scale; NDVI and slope are the key predictors explaining 36.2% of the SOC variability at the regional scale; and terrain factors are the most significant factors at the watershed scale. These three scales have a moderate spatial correlation in terms of SOC content. As the study scale widens, the spatial variability attributable to the random factors increases gradually, whereas the variability attributable to the structural factors gradually weakens. Soil type and land use type are the key factors influencing the SOC content at these three scales. At all scales, the SOC contents of the different land use types differ significantly in the order forestland &gt; shrubland &gt; grassland. Conservation of regional soil and water and prevention of soil desertification are effective measures for improving SOC content

Multiobjective Energy Consumption Optimization of a Flying–Walking Power Transmission Line Inspection Robot during Flight Missions Using Improved NSGA-II

In order to improve the flight efficiency of a flying–walking power transmission line inspection robot (FPTLIR) during flight missions, an accurate energy consumption model is constructed, and a multiobjective optimization approach using the improved NSGA-II is proposed to address the high energy consumption and long execution time. The energy consumption model is derived from the FPTLIR kinematics to the motor dynamics, with the key parameters validated using a test platform. A multiobjective optimization model is proposed that considers many constraints related to the FPTLIR during missions, offering a comprehensive analysis of the energy consumption and execution time. The NSGA-II algorithm is improved by integrating the Cauchy variation operator and the simulated annealing algorithm, which is used to construct the multiobjective optimization approach. Simulation and experimental results demonstrate that the proposed model accurately predicts the energy consumption of the FPTLIR across different paths and flight conditions with an average relative error ranging from 0.76% to 3.24%. After optimization, energy savings of 5.33% and 5.01% are achieved for on-line and off-line missions, respectively, while maintaining the shortest execution time at the given energy level. The energy consumption optimization approach significantly improves the flight efficiency of the system, providing a reference for analyzing and optimizing energy consumption of inspection robots

NaCl Promotes the Efficient Formation of Haematococcus pluvialis Nonmotile Cells under Phosphorus Deficiency

Natural astaxanthin helps reduce the negative effects caused by oxidative stress and other related factors, thereby minimizing oxidative damage. Therefore, it has considerable potential and broad application prospects in human health and animal nutrition. Haematococcus pluvialis is considered to be the most promising cell factory for the production of natural astaxanthin. Previous studies have confirmed that nonmotile cells of H. pluvialis are more tolerant to high intensity of light than motile cells. Cultivating nonmotile cells as the dominant cell type in the red stage can significantly increase the overall astaxanthin productivity. However, we know very little about how to induce nonmotile cell formation. In this work, we first investigated the effect of phosphorus deficiency on the formation of nonmotile cells of H. pluvialis, and then investigated the effect of NaCl on the formation of nonmotile cells under the conditions of phosphorus deficiency. The results showed that, after three days of treatment with 0.1% NaCl under phosphorus deficiency, more than 80% of motile cells had been transformed into nonmotile cells. The work provides the most efficient method for the cultivation of H. pluvialis nonmotile cells so far, and it significantly improves the production of H. pluvialis astaxanthin