Quantum linear systems algorithms: a primer
Quantum linear systems algorithms: a primer
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发表时间：
2018-02
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通讯作者：
Danial Dervovic;M. Herbster;P. Mountney;S. Severini;N. Usher;Leonard Wossnig
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作者：
Danial Dervovic;M. Herbster;P. Mountney;S. Severini;N. Usher;Leonard Wossnig
用于从线性系统解决方案采样的Harrow-Hassidim-lloyd（HHL）量子算法在其经典对应物上提供了指数加速。求解线性方程系统的问题具有广泛的应用范围，因此HHL构成了重要的算法原始。在这些注释中，我们详细介绍了HHL算法及其改进的版本，包括对组成型子例程的解释。更具体地说，我们通过量子RAM讨论了各种量子子例程，例如量子相估计和振幅扩增以及将数据加载到量子计算机中的重要问题。基于操作员使用Fourier and Chebyshev系列的分解，对原始算法利用可变时间振幅的改进以及一种实现单一操作（LCU）线性组合（LCU）的方法。最后，我们根据量子奇异值估计（QSVE）子例程讨论线性求解器。
The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of applications, and thus HHL constitutes an important algorithmic primitive. In these notes, we present the HHL algorithm and its improved versions in detail, including explanations of the constituent sub- routines. More specifically, we discuss various quantum subroutines such as quantum phase estimation and amplitude amplification, as well as the important question of loading data into a quantum computer, via quantum RAM. The improvements to the original algorithm exploit variable-time amplitude amplification as well as a method for implementing linear combinations of unitary operations (LCUs) based on a decomposition of the operators using Fourier and Chebyshev series. Finally, we discuss a linear solver based on the quantum singular value estimation (QSVE) subroutine.