发表机构
Virginia Tech（弗吉尼亚理工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出COFI-DQI方法，利用多种代数几何码扩展解码量子干涉算法，在最优函数交集问题中降低量子资源或增加约束数量。
AI 中文摘要
2025年，Jordan等人提出了解码量子干涉（DQI），这是一种基于解码的组合优化量子算法。他们考虑了里德-所罗门解码及其相关优化问题，称为最优多项式交集（OPI），该问题可视为有限域上的多项式回归问题。DQI在某些问题实例上展现出可证明的加速，并建立了解码问题与优化任务之间的联系。利用其他曲线族代数几何码的成熟对偶结构和解码理论，我们引入了COFI：基于曲线的最优函数交集。通过考虑两点Hermitian码、Suzuki码和扩展范数迹码，我们拓宽了DQI中使用的代数几何码的范围，并识别出在Jordan和Gu考虑的Hermitian最优多项式交集框架中，相比一点Hermitian码能提供进一步改进的曲线族。根据族和参数区域的不同，这些曲线可以减少量子资源需求或增加可考虑的约束数量。
英文摘要
In 2025, Jordan et al. introduced Decoded Quantum Interferometry (DQI), a quantum algorithm for combinatorial optimization based on decoding. They considered Reed-Solomon decoding and its associated optimization problem, called Optimal Polynomial Intersection (OPI), which may be viewed as a polynomial regression problem over a finite field. DQI exhibits provable speedups on certain problem instances and establishes a connection between decoding problems and optimization tasks. Leveraging the well-understood dual structure and decoding theory of algebraic geometry codes from other curve families, we introduce COFI: Curve-based Optimal Function Intersection. By considering two-point Hermitian codes, Suzuki codes, and extended norm-trace codes, we broaden the range of algebraic geometry codes used in DQI and identify families that offer further improvements over one-point Hermitian codes in the Hermitian Optimal Polynomial Intersection framework considered by Jordan and Gu. Depending on the family and parameter regime, these curves can reduce quantum resource requirements or increase the number of constraints that can be considered.
