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Lower Bounds for Local Search by Quantum Arguments Scott Aaronson

Summary: Lower Bounds for Local Search by Quantum Arguments
Scott Aaronson
The problem of finding a local minimum of a black-box func-
tion is central for understanding local search as well as quan-
tum adiabatic algorithms. For functions on the Boolean
hypercube {0, 1}n
, we show a lower bound of 2n/4
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
on the problem's classical ran-
domized 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.
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Source: Aaronson, Scott - Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (MIT)


Collections: Physics; Computer Technologies and Information Sciences