High-dimensional quantum Schur transforms
Adam Burchardt, Jiani Fei, Dmitry Grinko, Martin Larocca, Maris Ozols, Sydney Timmerman, Vladyslav Visnevskyi
量子舒尔变换已经成为一种基础量子算法,但即使在培根、庄和哈罗(BCH)2005年的论文发表开创性论文以来的二十年后,这种变换的某些方面仍然知之甚少。 此外,Krovi在2018年提出的替代方法最近被发现包含一个关键的错误。 在本文中,我们介绍了Krovi算法的校正版本以及BCH Schur变换的高维版本的详细处理。 这种高维焦点使得转换的两个版本适用于qudits n小于局部维度d的子制,Krovi的算法缩放为O(n^4),BCH为O(min(n^5,nd^4)。 我们的工作解决了文献中的一个关键空白,加强了在量子信息理论和量子计算中依赖Schur-Weyl二元性的广泛结果的算法基础。
The quantum Schur transform has become a foundational quantum algorithm, yet even after two decades since the seminal 2005 paper by Bacon, Chuang, and Harrow (BCH), some aspects of the transform remain insufficiently understood. Moreover, an alternative approach proposed by Krovi in 2018 was recently found to contain a crucial error. In this paper, we present a corrected version of Krovi's algorithm along with a detailed treatment of the high-dimensional version of the BCH Schur transform. This ...