论文标题
量子搜索算法的确切结果
Exact results on Quantum search algorithm
论文作者
论文摘要
我们在设置的密度矩阵中以两个任意阶段的两个任意阶段概括了Grover算法。我们为广义Grover操作员的任意迭代次数的迭代数量，作为迭代数量的函数，两个相角（α，\ {beta}）和参数ξ在密度矩阵的非对角线术语中引入的，有意义地捕获最初的量子量表中存在的相干性。我们扩展了Li和Li的想法，并显示了相匹配条件α= - \ {beta} =0.35π，带有两个迭代，并且我们可以实现成功概率> = 0.8，只有关于λ= 0.166的知识，其中λ是数据库中标记的总数态的比例。最后，我们量化了算法的成功概率，而在此简单模型中，初始量子状态的相干性降低了初始量子状态的相干性。
We generalize Grover algorithm with two arbitrary phases in a density matrix set up. We give exact analytic expressions for the success probability after arbitrary number of iteration of the generalized Grover operator as a function of number of iterations, two phase angles (α, \{beta}) and parameter ξ introduced in the off diagonal terms of the density matrix in a sense to capture the coherence present in the initial quantum register. We extend Li and Li's idea and show for the phase matching condition α = -\{beta} = 0.35π with two iterations and ξ = 1, we can achieve success probability >= 0.8 only with a knowledge about the lower bound of λ = 0.166 where λ is the ratio of marked to total number states in the database. Finally we quantify success probability of the algorithm with decrease in coherence of the initial quantum state against modest noise in this simple model.
