Quantum Walk Algorithm for Element Distinctness
نویسندگان
چکیده
منابع مشابه
Quantum Algorithms for Element Distinctness
We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard, Høyer, and Tapp, and imply an O(N3=4 logN) quantum upper bound for the element distinctness problem in the comparison complexity model. This contrasts with (N logN) classical complexity. We also prove a lower bound of ...
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The ELEMENT DISTINCTNESS problem is to decide whether each character of an input string is unique. The quantum query complexity of ELEMENT DISTINCTNESS is known to be Θ(N2/3); the polynomial method gives a tight lower bound for any input alphabet, while a tight adversary construction was only known for alphabets of size Ω(N2). We construct a tight Ω(N2/3) adversary lower bound for ELEMENT DISTI...
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The element distinctness problem is the problem of determining whether the elements of a list are distinct. Classically, it requires N queries, where N is the number of elements. In the quantum case, it is possible to solve the problem in O(N) queries. The problem can be extended by asking whether there are k colliding elements, known as element k-distinctness. This work obtains optimal values ...
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In a time-space tradeoff for sorting on non-oblivious machines, Borodin et. Al. [J. Comput. System Sci., 22(1981), pp. 351-364] proved that to sort $n$ elements requires $TS=\Omega(n^2)$ where $T=time$ and $S=space$ on a comparison based branching program. Although element distinctness and sorting are equivalent problems on a computation tree, the stated tradeoff result does not immediately fol...
متن کاملA Time-Efficient Quantum Walk for 3-Distinctness Using Nested Updates
We present an extension to the quantum walk search framework that facilitates quantum walks with nested updates. We apply it to give a quantum walk algorithm for 3-Distinctness with query complexity Õ(n), matching the best known upper bound (obtained via learning graphs) up to log factors. Furthermore, our algorithm has time complexity Õ(n), improving the previous Õ(n).
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2007
ISSN: 0097-5397,1095-7111
DOI: 10.1137/s0097539705447311