105 research outputs found

    A Faster Quantum Algorithm for Semidefinite Programming via Robust IPM Framework

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    This paper studies a fundamental problem in convex optimization, which is to solve semidefinite programming (SDP) with high accuracy. This paper follows from existing robust SDP-based interior point method analysis due to [Huang, Jiang, Song, Tao and Zhang, FOCS 2022]. While, the previous work only provides an efficient implementation in the classical setting. This work provides a novel quantum implementation. We give a quantum second-order algorithm with high-accuracy in both the optimality and the feasibility of its output, and its running time depending on log(1/ϵ)\log(1/\epsilon) on well-conditioned instances. Due to the limitation of quantum itself or first-order method, all the existing quantum SDP solvers either have polynomial error dependence or low-accuracy in the feasibility

    Some Predictions of Deformations from Tram Track Construction in a Structure-Embankment Transition Zone

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    AbstractBased on a construction project of a tram line in Nanjing City of China, the influence of a tram track construction on the deformation characteristics of an adjacent metro station and tunnels is investigated. Because a section of the tram track is designed to be constructed in the vicinity of the connection between a metro station and metro tunnels, the foundation of the tram track is changed from the station structure to the normal embankment. As a result, deformations from tram track construction in this structure-embankment transition zone will be serious. In order to protect the metro station and the twin tunnels from the construction-induced deformation and long term settlement caused by tram trains, a recommended treatment of the structure-embankment transition zone is suggested according to the property of the surrounding soils. The construction process of the tram track over the metro station and the tunnels is simulated by a finite element analysis (FEA) method. The deformation characteristics of the metro station and tunnels are calculated. Results indicate that with the recommended transition zone design the deformation response of the adjacent underground structures can be well controlled and the transition performance of the tram track transition zone can be improved