线性方程组的量子循环预条件子
Quantum Circulant Preconditioner for Linear System of Equations
摘要：
我们考虑带有循环预条件子$C$的$Ax=b$的量子线性求解器。主要的技术是奇异值估计（SVE）在[I。Kerenkirst和A. Prakash，Quantum推荐系统，ITCS 2017]。然而，SVE的一些修改应作出解决预处理的线性系统$C^{-1} Ax = C^{-1} b$。而且，不同于[B. D.克拉德湾C.雅各布斯角R. Sprouse，预条件量子线性系统算法，物理评论快报，2013]，循环预条件子易于构造，可直接应用于一般稠密非厄米特情形.时间复杂度取决于$C$和$C^{-1} A$的条件数，以及Frobenius范数$\|A\|_F$。
英文摘要：
We consider the quantum linear solver for $Ax=b$ with the circulant preconditioner $C$. The main technique is the singular value estimation (SVE) introduced in [I. Kerenidis and A. Prakash, Quantum recommendation system, in ITCS 2017]. However, some modifications of SVE should be made to solve the preconditioned linear system $C^{-1} Ax = C^{-1} b$. Moreover, different from the preconditioned linear system considered in [B. D. Clader, B. C. Jacobs, C. R. Sprouse, Preconditioned quantum linear system algorithm, Phys. Rev. Lett., 2013], the circulant preconditioner is easy to construct and can be directly applied to general dense non-Hermitian cases. The time complexity depends on the condition numbers of $C$ and $C^{-1} A$, as well as the Frobenius norm $\|A\|_F$.
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。
