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We present quantum algorithms for routing concentration assignments on fullcapacity fat-and-slim concentrators, bounded fat-and-slim concentrators, andregular fat-and-slim concentrators. Classically, the concentration assignmenttakes $O(n)$ time on all these concentrators, where $n$ is the number ofinputs. Powered by Grover's quantum search algorithm, our algorithms take$O(\sqrt{nc}\ln{c})$ time, where $c$ is the capacity of the concentrator. Thus,our quantum algorithms are asymptotically faster than their classicalcounterparts, when $c\ln^2{c}=o(n)$.In general, $c = n^\mu,$ satisfies$c\ln^2{c}=o(n),$ implying a time complexity of $O(n^{0.5(1+ \mu )} \ln n),$for any $\mu, 0 < \mu < 1.$

Faster Quantum Concentration via Grover's Search