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The optimality of Grover's algorithm doesn't in any way suggest that the upper bound on speedup is quadratic. That result only applies to one very particular c
by michael_nielsen 16y ago
The optimality of Grover's algorithm doesn't in any way suggest that the upper bound on speedup is quadratic. That result only applies to one very particular class of problems: unstructured (oracle) search problems. There are other oracle problems for which the speedup is known to be exponential. For non-oracle problems the situation isn't yet clear, although many people believe the speedup will be exponential. That will be true if factoring isn't in BPP, for instance.