  Long-lived quantum speedup serves as a fundamental component for quantum
algorithms. The quantum walk is identified as an ideal scheme to realize the
long-lived quantum speedup. However, one finds that the duration of quantum
speedup is very short in real systems implementing quantum walk. The speedup
can last only dozens of femtoseconds in the photosynthetic light-harvesting
system, which was regarded as the best candidate for quantum information
processing. Here, we construct one plasmonic system with two-level molecules
embodied in the hot spots of one-dimensional nanoparticle chains to realize the
long-lived quantum speedup. The coherent and incoherent coupling parameters in
the system are obtained by means of Green's tensor technique. Our results
reveal that the duration of quantum speedup in our scheme can exceed 500 fs
under strong coherent coupling conditions, which is several times larger than
that in the photosynthetic light-harvesting system. Our proposal presents a
competitive scheme to realize the long-lived quantum speedup, which is very
beneficial for quantum algorithms.
