Quickly obtaining optimal solutions of combinatorial optimization problems has tremendous value but is extremely difficult. Thus, various kinds of machines specially designed for combinatorial optimization have recently been proposed and developed. Toward the realization of higher-performance machines, here, we propose an algorithm based on classical mechanics, which is obtained by modifying a previously proposed algorithm called simulated bifurcation. Our proposed algorithm allows us to achieve not only high speed by parallel computing but also high solution accuracy for problems with up to one million binary variables. Benchmarking shows that our machine based on the algorithm achieves high performance compared to recently developed machines, including a quantum annealer using a superconducting circuit, a coherent Ising machine using a laser, and digital processors based on various algorithms. Thus, high-performance combinatorial optimization is realized by massively parallel implementations of the proposed algorithm based on classical mechanics.
We report a synthesis of a closely packed multi-walled carbon nanotube (MWCNT) forest by a multi-step growth method, including a new approach to immobilize catalytic nanoparticles, using plasma-based chemical vapor deposition. The CNT packing density reaches one-half of the theoretical value, where the space of 30–40% is filled with MWCNTs. This value is approximately one order of magnitude larger than that of as-grown CNT forest synthesized using conventional methods. The method is applicable even at a spatially restricted region, for example, in trench or via hole, and is available at the growth temperature as low as 450 °C.
A method including surface silanization, phase transfer and self-assembly, and SiO2 shell growth has been developed to incorporate multiple hydrophobic CdSe/ZnS nanocrystals into SiO2 beads where they are well suited for bio-application due to their high brightness, less-cytotoxic, and non-blinking nature.
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