半定规划有序搜索问题的改进量子算法
Improved quantum algorithms for the ordered search problem via semidefinite programming
摘要：
最基本的计算问题之一是在N个项目的有序列表中找到所需的项目。虽然这个问题的最佳经典算法使用log_2 N查询列表，量子计算机可以解决这个问题，使用一个常数因子更少的查询。然而，这个常数的精确值是未知的。通过半定规划描述一类有序搜索的量子查询算法，我们发现了新的量子算法的有序搜索问题的小实例。扩展这些算法到任意大的情况下使用递归，我们表明，有一个确切的量子有序搜索算法，使用4 log_{605} N \approx 0.433 log_2 N查询，这提高了以前最好的已知精确算法。
英文摘要：
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log_2 N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for ordered search in terms of a semidefinite program, we find new quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log_{605} N \approx 0.433 log_2 N queries, which improves upon the previously best known exact algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
