Hybrid algorithms to solve linear systems of equations with limited qubit resources

The solution of linear systems of equations is a very frequent operation and thus important in many fields. The complexity using classical methods increases linearly with the size of equations. The HHL algorithm proposed by Harrow et al. achieves exponential acceleration compared with the best classical algorithm. However, it has a relatively high demand for qubit resources and the solution $\left| x \right\rangle$ is in a normalized form. Assuming that the eigenvalues of the coefficient matrix of the linear systems of equations can be represented perfectly by finite binary number strings, three hybrid iterative phase estimation algorithms (HIPEA) are designed based on the iterative phase estimation algorithm in this paper. The complexity is transferred to the measurement operation in an iterative way, and thus the demand of qubit resources is reduced in our hybrid algorithms. Moreover, the solution is stored in a classical register instead of a quantum register, so the exact unnormalized solution can be obtained. The required qubit resources in the three HIPEA algorithms are different. HIPEA-1 only needs one single ancillary qubit. The number of ancillary qubits in HIPEA-2 is equal to the number of nondegenerate eigenvalues of the coefficient matrix of linear systems of equations. HIPEA-3 is designed with a flexible number of ancillary qubits. The HIPEA algorithms proposed in this paper broadens the application range of quantum computation in solving linear systems of equations by avoiding the problem that quantum programs may not be used to solve linear systems of equations due to the lack of qubit resources.Comment: 22 pages, 6 figures, 6 tables, 48 equation

Optical and molecular diversity of dissolved organic matter in sediments of the Daning and Shennong tributaries of the Three Gorges Reservoir

Introduction: Damming significantly modifies the function of natural river networks and influences sediment dynamics with a reservoir’s operation. The dissolved organic matter (DOM) in reservoir sediments severely affects carbon flow from land to sea. However, the properties of DOM (e.g., quantity and quality) in reservoir sediments and their relationship with carbon cycling remain unclear as complex reservoir construction interrupts the environmental processes.Methods: This study characterizes the optical and molecular properties of sediment water-extractable organic matter (WEOM) in the Daning and Shennong tributaries of the world’s largest reservoir—the Three Gorges Reservoir (TGR)—by applying optical techniques and ultrahigh-resolution Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS).Results and Discussion: We first assessed the link between light-absorbing components and the individual molecules in WEOM, which were significantly different than DOM in water and indicated that there might be an intrinsic variation between DOM in sediment and in water. Then, with the unique optical–molecular property linkage assessed, multiple sources (autochthonous and terrestrial) were identified, and a declining trend of terrestrial and recalcitrant WEOM was revealed from the tributaries upstream to downstream. Finally, through covariance analysis of the properties between WEOM and sediment particles, we demonstrated that the WEOM dynamic was most likely regulated by hydrologic sorting-induced particle size and mineral composition variations of sediment. Moreover, assessment between lability and WEOM molecular properties suggested that the WEOM dynamic likely contributes to carbon burial in the reservoir. This study emphasizes the influence of dam construction on organic matter accumulation and riverine carbon cycling

Anthropogenic Aerosols Cause Recent Pronounced Weakening of Asian Summer Monsoon Relative to Last Four Centuries

The Asian Summer Monsoon (ASM) affects ecosystems, biodiversity, and food security of billions of people. In recent decades, ASM strength (as represented by precipitation) has been decreasing, but instrumental measurements span only a short period of time. The initiation and the dynamics of the recent trend are unclear. Here for the first time, we use an ensemble of 10 tree ring-width chronologies from the west-central margin of ASM to reconstruct detail of ASM variability back to 1566 CE. The reconstruction captures weak/strong ASM events and also reflects major locust plagues. Notably, we found an unprecedented 80-year trend of decreasing ASM strength within the context of the 448-year reconstruction, which is contrary to what is expected from greenhouse warming. Our coupled climate model shows that increasing anthropogenic sulfate aerosol emissions over the Northern Hemisphere could be the dominant factor contributing to the ASM decrease. Plan Language Summary Monsoonal rainfall has a certain influence on agriculture and industry in the regions of Asian Summer Monsoon (ASM). An understanding of the spatial-temporal variability of the ASM and the associated dynamics is vital for terrestrial ecosystems, water resources, forests, and landscapes. We have developed a 448-year ASM reconstruction back to 1566 CE using 10 tree ring chronologies from the margin region of ASM. We find that historical severe droughts and locust plague disasters during weak ASM events. The recent decreasing ASM trend persisting for over 80 years is unprecedented over the past 448 years. Coupled climate models show that increasing anthropogenic aerosol emissions are the dominant underlying factor. Our aim is that the time series will find a wide range of utility for understanding past climate variability and for predicting future climate change.National Natural Science Foundation of China [41630531]; National Research Program for Key Issues in Air Pollution Control [DQGG0104]; Chinese Academy of Sciences [QYZDJ-SSW-DQC021, XDPB05, GJHZ1777]; Institute of Earth Environment, Chinese Academy of Sciences; State Key Laboratory of Loess and Quaternary Geology6 month embargo; first published: 09 April 2019This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Solving DC Power Flow Problems Using Quantum and Hybrid algorithms

Power flow calculation plays an important role in planning, operation, and control of the power system. The quantum HHL algorithm can achieve theoretical exponential speedup over classical algorithms on DC power flow calculation. Since the qubit resources in the Noisy Intermediate-scale Quantum (NISQ) era are limited, it is important to discuss the performance considering this limitation. The coefficient matrix of the linear systems of equations in DC power flow problems cannot be represented perfectly by finite binary number strings, which leads to imperfect phase estimation. This work is carried out under the assumption of imperfect phase estimation. The performance of the HHL algorithm is systematically investigated with different accuracy and redundant qubits. In order to further reduce the required qubit resources, a hybrid quantum-classical algorithm is proposed. By comparing errors of the HHL and hybrid algorithms in the DC power flow calculation of the IEEE 5-bus test system, it is found that the hybrid algorithm can achieve comparable precision with fewer qubits than HHL by increasing the number of phase estimation modules, which may make the hybrid algorithm a feasible route in the NISQ era.Comment: 17 pages, 8 figures, 2 tables, 32 equation

Numerical Study on the Surface Movement Regularity of Deep Mining Underlying the Super-Thick and Weak Cementation Overburden: A Case Study in Western China

While surface movement regularities have been sufficiently understood in the mining practices of eastern China, the case seems to be very different in western China where the super-thick and weak cementation (STWC) overburden exists. To better understand such knowledge, we compared geomining conditions and surface subsidence data for 16 coal mines and developed a carefully calibrated numerical model, with primary concern the relationship between subsidence rate and mining scale. We find that mining under the STWC overburden is characterized by the extremely small subsidence rate compared to the deep mining cases in eastern China, and the unusual subsidence phenomenon should be regional rather than an isolated case. We also find that the critical subsidence basin can be formed only when the goaf length and width both reach about 3.3 h (h is the average mining depth), which is far beyond the conventional understanding. We suggest that the large-scale mining under the STWC overburden carries enormous risks, which require great attention. The reported data, findings, and suggestions in this paper should be quite useful for coal mines with similar geomining conditions, and are also important for ecological protection and sustainable development of western China

Mobile robot motion control and autonomous navigation in GPS-denied outdoor environments using 3D laser scanning

Purpose This paper aims to propose a series of approaches to solve the problem of the mobile robot motion control and autonomous navigation in large-scale outdoor GPS-denied environments. Design/methodology/approach Based on the model of mobile robot with two driving wheels, a controller is designed and tested in obstacle-cluttered scenes in this paper. By using the priori "topology-geometry" map constructed based on the odometer data and the online matching algorithm of 3D-laser scanning points, a novel approach of outdoor localization with 3D-laser scanner is proposed to solve the problem of poor localization accuracy in GPS-denied environments. A path planning strategy based on geometric feature analysis and priority evaluation algorithm is also adopted to ensure the safety and reliability of mobile robot's autonomous navigation and control. Findings A series of experiments are conducted with a self-designed mobile robot platform in large-scale outdoor environments, and the experimental results show the validity and effectiveness of the proposed approach. Originality/value The problem of motion control for a differential drive mobile robot is investigated in this paper first. At the same time, a novel approach of outdoor localization with 3D-laser scanner is proposed to solve the problem of poor localization accuracy in GPS-denied environments. A path planning strategy based on geometric feature analysis and priority evaluation algorithm is also adopted to ensure the safety and reliability of mobile robot's autonomous navigation and control