在量子计算机上玩Mastermind
Playing Mastermind on quantum computers
摘要：
从20世纪70年代至今，经典的双人游戏《摄魂师》吸引了大量的关注，不仅作为一款流行游戏受到公众的关注，而且作为一个科学问题也受到学术界的关注。具有n个位置和k种颜色的Mastermind的形式描述为：编码者私下选择一个秘密$s\in [k]^n$，并且解码者希望在尽可能少的查询中确定$s$，如$f_s(x)$，其中$f_s(x)$指示x如何接近s。策略的复杂性是通过使用的查询数量来衡量的。在这项工作中，我们研究了在非自适应和自适应设置下在量子计算机上玩Mastermind，获得高效的量子算法，这些算法都是精确的（即，肯定返回正确的结果），并显示出巨大的量子加速。从技术上讲，我们开发了一个三步框架来设计一般字符串学习问题的量子算法，这不仅可以在玩Mastermind时实现巨大的量子加速，而且还可以为其他字符串学习问题探索量子加速。
英文摘要：
From the 1970s up to now, Mastermind, a classic two-player game, has attracted plenty of attention, not only from the public as a popular game, but also from the academic community as a scientific issue. Mastermind with n positions and k colors is formally described as: the codemaker privately chooses a secret $s\in [k]^n$, and the coderbreaker want to determine $s$ in as few queries like $f_s(x)$ as possible to the codemaker, where $f_s(x)$ indicates how x is close to s. The complexity of a strategy is measured by the number of queries used. In this work we study playing Mastermind on quantum computers in both non-adaptive and adaptive settings, obtaining efficient quantum algorithms which are all exact (i.e., return the correct result with certainty) and show huge quantum speedups. Technically, we develop a three-step framework for designing quantum algorithms for the general string learning problem, which not only allows huge quantum speedups on playing Mastermind, but also may shed light on exploring quantum speedups for other string learning problems.
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。
