Quantum computing is a new computing model based on the principles of quantum mechanics. Because of its powerful parallelism far superior to classical computing, quantum computing is considered as a computational method that may have a subversive impact on the future, providing a new way to solve some complex problems. The algorithms and applications of quantum solvers in numerical computation-related problems of large-scale science and engineering are reviewed. In particular, systems of linear equations, eigenvalue problems, differential equations, Hamiltonian and graph computation, quantum machine learning, quantum solver platform, and practical numerical simulation have been introduced. Aiming at different numerical computing problems, the current mainstream quantum computing algorithms are introduced in detail, and the research progress of relevant algorithms at home and abroad in recent years is comprehensively summarized. Finally, the future development trend of quantum computing in numerical algebra solving is prospected.
By dividing the community of the power grid, the information network community is divided according to the current situation and the actual coupling relationship of the corresponding hierarchical partition construction of the power grid and the information network, and the node with the largest betweenness and the node with the largest degree of each community in the information network is selected for full connection. The power information interdependence network model based on the hybrid point-to-point structure of the blockchain, combined with the consensus mechanism of the blockchain, analyzes the advantages of the model, and uses the two attack strategies of high number attack and high betweenness attack to study the proposed interdependence The robustness of the network is compared with the traditional centralized control power information network and the fully decentralized point-to-point power information network. The research results show that the hybrid point-to-point power information interdependence network model can effectively reduce the communication overhead and consensus delay of the practical Byzantine fault-tolerant algorithm on the basis of improving the robustness of the network. In the hybrid peer-to-peer power information network, the system shows stronger vulnerability under the high-number attack mode.
Izhikevich neuronal model is based on the modeling of cortical and thalamic neurons. This model has the characteristics of being closer to the discharge properties of real biological neurons and it is convenient for large-scale simulation. A square neural network composed of 200 × 200 Izhikevich neurons is constructed under random boundary conditions in this paper, the computer simulation method is used to calculate the spatiotemporal characteristics and synchronization factor of the square network, and the firing patterns and bifurcation phenomena of neurons, as well as the spatiotemporal patterns and synchronization properties of the square network are studied. The results show that in the square neural network constructed by Izhikevich neurons with different discharge modes under the same current stimulation and coupling intensity, the emergence and disappearance of spiral wave seeds can be observed in the neural network only when the neurons are in the Regular Spiking discharge mode. On the other hand, spiral wave seeds cannot be observed in the square neural network constructed by Izhikevich neurons with other discharge modes (e.g. Fast Spiking, Chattering, Internally Bursting). When the external current stimulation is constant, only the medium-sized coupling strength between neurons can induce the emergence and extinction of spiral wave seeds in the square neural network, and smaller or larger coupling strength cannot induce spiral wave seeds in the neural network. In addition, the synchronization factor in square neural networks has been investigated.
An algebraic multigrid (AMG) algorithm based on hybrid coarsening is proposed for the linear systems of the discrete pressure Poisson which is derived from the SIMPLE algorithm for the Navier-Stokes equations in complex flows. This algorithm combines a class of non-smoothed aggregation coarsening with classical C/F coarsening to construct grid hierarchy, hoping to reduce the cost in the setup phase of the AMG algorithm without affecting convergence. The high performance of the proposed algorithm is verified by numerical simulation of complex flow in the combustion chamber of aero-engine. The results show that the proposed algorithm can achieve 78% acceleration compared with the classical AMG algorithm.
A highly accuracy internally multi-reference configuration interaction method (icMRCI) was used to calculate potential curves of low-lying electronic states and transition dipole moment of A3П-X3Σ- system for OH+ ion. Davidson correction (MRCI+Q) of energy and scalar relativistic effect were considered in the calculation. Based on potential energy curves of low-lying electronic states spectroscopic parameters were determined by solving one-dimensional radial Schr dinger equation of nuclear motion. Einstein coefficient and F-C factor of A3П-X3Σ- transition system are calculated by using the transition dipole moment. Moreover, radiative lifetimes of A3П(ν'=0-6) vibration states were studied. It shows that the radiative lifetimes are of the order of 10-6 s.
