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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 [n]d. Our lower bound is nearly tight, as Grover Search can be used to find a fixed point with O(nd/2) quantum queries. Our result establishes a nearly tight bound for the computation of d-dimensional approximate Brouwer fixed points defined by Scarf and by Hirsch,...
The quantum query complexity of searching for local optima has been a subject of much interest in the recent literature. For the d-dimensional grid graphs, the complexity has been determined asymptotically for all fixed d≥5, but the lower dimensional cases present special difficulties, and considerable gaps exist in our knowledge. In the present paper we present near-optimal lower bounds, showing...
The quantum query complexity of searching for local optima has been a subject of much interest in the recent literature. For the d-dimensional grid graphs, the complexity has been determined asymptotically for all fixed d ges 5, but the lower dimensional cases present special difficulties, and considerable gaps exist in our knowledge. In the present paper we present near-optimal lower bounds, showing...
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