Faster Quantum Concentration via Grover's Search
share
We present quantum algorithms for routing concentration assignments on full capacity fat-and-slim concentrators, bounded fat-and-slim concentrators, and regular fat-and-slim concentrators. Classically, the concentration assignment takes O(n) time on all these concentrators, where n is the number of inputs. Powered by Grover's quantum search algorithm, our algorithms take O(√(nc)lnc) time, where c is the capacity of the concentrator. Thus, our quantum algorithms are asymptotically faster than their classical counterparts, when cln^2c=o(n).In general, c = n^μ, satisfies cln^2c=o(n), implying a time complexity of O(n^0.5(1+ μ )ln n), for any μ, 0 < μ < 1.
READ FULL TEXT