The embedding is an essential step when calculating on the D-Wave machine. In this work we show the hardness of the embedding problem for both types of existing hardware, represented by the Chimera and the Pegasus graphs, containing unavailable qubits. We construct certain broken Chimera graphs, where it is hard to find a Hamiltonian cycle. As the Hamiltonian cycle problem is a special case of the embedding problem, this proves the general complexity result for the Chimera graphs. By exploiting the subgraph relation between the Chimera and the Pegasus graphs, the proof is then further extended to the Pegasus graphs.
Developments in numerical simulation of flows and high performance computing influence one another. More detailed simulation methods create a permanent need for more computational power, while new hardware developments often require changes to the software to exploit new hardware features.This dependency is very pronounced in the case of vector-units which are featured by all modern processors to increase their numerical throughput but require vectorization of the software to be used efficiently. We study the vectorization of a simulation method that exhibits an inherent level of vector-parallelism. This is of particular interest as SIMD operations will hopefully be available with std::simd in a future C++ standard.The simulation method considered here results in the simultaneous solution of multiple sparse linear systems of equations which only differ by their main diagonal and right hand sides. Such structure arises in the simulation of unsteady flow in turbomachinery by means of a frequency domain approach called harmonic balance.
Developments in numerical simulation of flows and high-performance computing influence one another. More detailed simulation methods create a permanent need for more computational power, while new hardware developments often require changes to the software to exploit new hardware features. This dependency is very pronounced in the case of vector-units which are featured by all modern processors to increase their numerical throughput but require vectorization of the software to be used efficiently. We study the vectorization of a simulation method that exhibits an inherent level of vector-parallelism. This is of particular interest as SIMD operations will hopefully be available with std::simd in a future C++ standard. The simulation method considered here results in the simultaneous solution of multiple sparse linear systems of equations which only differ by their main diagonal and right-hand sides. Such structure arises in the simulation of unsteady flow in turbomachinery by means of a frequency domain approach called harmonic balance.
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