论文标题
HyperCube量子搜索：多项式时间中成功概率的精确计算
Hypercube Quantum Search: Exact Computation of the Probability of Success in Polynomial Time
论文作者
论文摘要
在量子算法的新兴领域中，Grover的量子搜索无疑是最重要的量子之一。它相对简单，执行有用的任务，更重要的是，它以最佳方式进行。但是，由于该领域的量子步行成功，研究量子搜索变体在几种步行中都是合乎逻辑的。在本文中，我们提出了对超立方体布局的量子搜索的深入研究。首先，通过对限于合适特征空间的基本步行操作员的分析，我们表明搜索算法的作用组件发生在希尔伯特工作区的一个小子空间中，该子空间随问题大小线性增长。随后，我们利用此属性来预测多项式时间量子搜索成功概率的确切演变。
In the emerging domain of quantum algorithms, the Grover's quantum search is certainly one of the most significant. It is relatively simple, performs a useful task and more importantly, does it in an optimal way. However, due to the success of quantum walks in the field, it is logical to study quantum search variants over several kind of walks. In this paper, we propose an in-depth study of the quantum search over a hypercube layout. First, through the analysis of elementary walk operators restricted to suitable eigenspaces, we show that the acting component of the search algorithm takes place in a small subspace of the Hilbert workspace that grows linearly with the problem size. Subsequently, we exploit this property to predict the exact evolution of the probability of success of the quantum search in polynomial time.
