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Lower bounds for local search by quantum arguments

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Lower bounds for local search by quantum arguments
The problem of finding a local minimum of a black-box function is central for understanding local search as well as quantum adiabatic algorithms. For functions on the Boolean hypercube {0, 1}n , we show a lower bound of 2n/4 /n on the number of queries needed by a quantum computer to solve this problem. More surprisingly, our approach, based on Ambainis's quantum adversary method, also yields a lower bound of 2n/2 /n2 on the problem's classical randomized query complexity. This improves and simplifies a 1983 result of Aldous. Finally, in both the randomized and quantum cases, we give the first nontrivial lower bounds for finding local minima on grids of constant dimension d 3. Categories and Subject Descriptors
Scott Aaronson
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2004
Where STOC
Authors Scott Aaronson
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