Year: 1999
Type: preprint
Abstract: We consider the problem where P is an unknown permutation on {0,1,...,2^n - 1}, y is an element of {0,1,...,2^n - 1}, and the goal is to determine the minimum r > 0 such that P^r(y) = y (where P^r is P composed with itself r times). Information about P is available only via queries that yield P^x(y) from any x in {0,1,...,2^m - 1} and y in {0,1,...,2^n - 1} (where m is polynomial in n). The main resource under consideration is the number of these queries. We show that the number of queries necessary to solve the problem in the classical probabilistic bounded-error model is exponential in n. This contrasts sharply with the quantum bounded-error model, where a constant number of queries suffices.
Source: arXiv (Cornell University)
Author: Cleve, Richard
Institution: University of Calgary
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950569197