Quantum lower bound for sorting

Abstract

We prove that Ω(n log(n)) comparisons are necessary for any quantum algorithm that sorts n numbers with high success probability and uses only comparisons. If no error is allowed, at least 0.110nlog_2(n) - 0.067n + O(1) comparisons must be made. The previous known lower bound is Ω(n).

This paper has been merged with another paper. See quant-ph/0102078