Can quantum search accelerate evolutionary algorithms?
Proceedings of the 12th annual conference on Genetic and evolutionary computation
Time space tradeoffs for attacks against one-way functions and PRGs
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Postselection finite quantum automata
UC'10 Proceedings of the 9th international conference on Unconventional computation
Quantum and randomized lower bounds for local search on vertex-transitive graphs
Quantum Information & Computation
The limits of quantum computers
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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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 $\left\{0,1\right\}^n$, we show a lower bound of $\Omega\left(2^{n/4}/n\right)$ 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 $\Omega\left(2^{n/2}/n^2\right)$ 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 $d\geq3$.