Optimized quantum random-walk search algorithms on the hypercube
نویسندگان
چکیده
منابع مشابه
Optimized quantum random-walk search algorithms
Shenvi, Kempe and Whaley’s quantum random-walk search (SKW) algorithm [2003 Phys. Rev. A 67 052307] is known to require O( √ N) number of oracle queries to find the marked element, where N is the size of the search space. This scaling is thought to be the best achievable on a quantum computer. We prove that the final state of the quantum walk in the SKW algorithm yields the nearest neighbours o...
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We investigate a set of discrete-time quantum search algorithms on the n-dimensional hypercube following a proposal by Shenvi, Kempe and Whaley [1]. We show that there exists a whole class of quantum search algorithms in the symmetry reduced space which perform a search of a marked vertex in time of order √ N where N = 2, the number of vertices. In analogy to Grover’s algorithm, the spatial sea...
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In the last lecture we analyzed a random walk on a truncated cube, where Ω = {x ∈ {0, 1}|∑ni=1 aixi ≤ b}. The mixing time of this random walk can be shown to be O(n), where n is the dimension of the cube [MS99]. We presented a slightly simplified analysis that gave a mixing time bound of n 2), under the assumption that 1 ≤ max |ai| ≤ B (i.e., the ratio of the weights is bounded). We used a flow...
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ژورنال
عنوان ژورنال: Physical Review A
سال: 2009
ISSN: 1050-2947,1094-1622
DOI: 10.1103/physreva.79.012325