多值量子算法的应用
Applications of Multi-Valued Quantum Algorithms
AI总结：
本文利用量子傅里叶变换将 Deutsch-Jozsa 与 Grover 算法推广至 n 值逻辑，实现单次函数判别、仿射函数闭式求解，并降低搜索算法的 qudit 与存储需求。
摘要：
本文利用量子傅里叶变换，将二进制的 Deutsch-Jozsa 算法和 Grover 算法推广到 n 值逻辑。我们扩展后的 Deutsch-Jozsa 算法不仅能够在单次查询中区分常量布尔函数和平衡布尔函数，还可以求出量子预言机中各类仿射逻辑函数的闭式表达式，精度达到一个常数项。此外，我们针对量子数据库搜索提出的 Grover 算法多值扩展在实现时需要更少的 qudit，因而所需的存储寄存器显著更小，浪费的信息状态也更少。我们指出了这些算法的若干应用及其相对于二进制情形的优势。
英文摘要：
This paper generalizes both the binary Deutsch-Jozsa and Grover algorithms to $n$-valued logic using the quantum Fourier transform. Our extended Deutsch-Jozsa algorithm is not only able to distinguish between constant and balanced Boolean functions in a single query, but can also find closed expressions for classes of affine logical functions in quantum oracles, accurate to a constant term. Furthermore, our multi-valued extension of the Grover algorithm for quantum database search requires fewer qudits and hence a substantially smaller memory register, as well as fewer wasted information states, to implement. We note several applications of these algorithms and their advantages over the binary cases.
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。
