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Quantum Separation of Local Search and Fixed Point Computation
2009
Algorithmica
In this paper, we give a lower bound of Ω(n (d−1)/2 ) on the quantum query complexity for finding a fixed point of a discrete Brouwer function over grid [1 : n] d . Our bound is nearly tight, as the Grover search algorithm can be used to find a fixed point with O(n d/2 ) quantum queries. Our result establishes a nearly tight bound for the computation of d-dimensional approximate Brouwer fixed points as defined by Scarf and by Hirsch, Papadimitriou, and Vavasis. It can also be extended to the
doi:10.1007/s00453-009-9289-0
fatcat:c363o34j5fezvpyql7gpu7n25e