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Minimum weight
About: Minimum weight is a research topic. Over the lifetime, 2002 publications have been published within this topic receiving 28244 citations.
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TL;DR: In this paper, the propagation of errors in space and time by the two-qubit interactions is taken into account, which leads to a quadratic improvement of the logical error rate.
Abstract: The surface code is a powerful quantum error correcting code that can be defined on a2-D square lattice of qubits with only nearest neighbor interactions Syndrome and dataqubits form a checkerboard pattern Information about errors is obtained by repeat-edly measuring each syndrome qubit after appropriate interaction with its four nearestneighbor data qubits Changes in the measurement value indicate the presence of chainsof errors in space and time The standard method of determining operations likely toreturn the code to its error-free state is to use the minimum weight matching algorithmto connect pairs of measurement changes with chains of corrections such that the min-imum total number of corrections is used Prior work has not taken into account thepropagation of errors in space and time by the two-qubit interactions We show thattaking this into account leads to a quadratic improvement of the logical error rate
18 citations
TL;DR: In this article, a method for the minimum weight design of practical planar frameworks under both service and ultimate loading conditions is presented. Acceptable elastic stresses and displacements are ensured at the service-load level while, simultaneously, adequate safety against plastic collapse at the ultimate load level is ensured.
18 citations
TL;DR: All extremal binary self-dual [50,25,10] codes with an automorphism of order 7 are enumerated and the minimum weight codewords yield quasi-symmetric 2-(49,9,6) designs.
Abstract: All extremal binary self-dual [50,25,10] codes with an automorphism of order 7 are enumerated. Up to equivalence, there are four such codes, three with full automorphism group of order 21, and one code with full group of order 7. The minimum weight codewords yield quasi-symmetric 2-(49,9,6) designs.
18 citations
TL;DR: In this article, exact upper bounds for the minimum weight of minor faces in normal plane maps and 3-polytopes with specified maximum vertex degree were obtained for the case of 3 polytopes.
Abstract: Precise upper bounds are obtained for the minimum weight of minor faces in normal plane maps and 3-polytopes with specified maximum vertex degree.
18 citations
TL;DR: In this paper, an angle-ply laminated plate is optimized with the objective of minimizing its weight subject to maximum deflection and buckling constraints, where the shape of the initial deflection is not known a priori, and as such it is uncertain.
Abstract: An angle-ply laminated plate is optimized with the objective of minimizing its weight subject to maximum deflection and buckling constraints. The plate has an initial deflection the shape of which is not known a priori, i.e., the initial deflection is not specified in a deterministic manner and as such it is uncertain. The weight is proportional to the laminate thickness which is minimized taking the ply angles as design variables and under the least favorable conditions of initial imperfections. The convex modeling approach is employed to analyze the uncertain initial deflection with the uncertain quantities allowed to vary arbitrarily around their average values subject to the requirement that these variations are bounded in L 2 norm. The results are given for both single load and multiple load cases and the effect of uncertainty on the optimal design is investigated. It is shown that the minimum weight increases with increasing level of uncertainty and the optimal ply angles also depend on the level of uncertainty.
18 citations