论文标题
参数估计不情愿的量子步行：最大似然方法
Parameter Estimation with Reluctant Quantum Walks: a Maximum Likelihood approach
论文作者
论文摘要
参数最大似然估计问题问题在量子步行理论的背景下解决了整数晶格的量子行走。提出了硬币动作，并用正交重组矩阵的角度参数估算的真实参数$θ$。我们为$ d $ j $ steps之后的量子步行者的概率分布提供了分析结果。对于$ k $大的，我们表明，以比率$ d/k $确定的位移达到高峰，这与重新安装参数$θ$相关。我们建议这种“不情愿的步行者”行为为最大似然估计分析提供了框架，从而通过封闭进化环路的回报概率和量子测量量估计了$θ$的稳健参数估计，以及用“递减量指数”的量子步行器位置的量子测量值。
The parametric maximum likelihood estimation problem is addressed in the context of quantum walk theory for quantum walks on the lattice of integers. A coin action is presented, with the real parameter $θ$ to be estimated identified with the angular argument of an orthogonal reshuffling matrix. We provide analytic results for the probability distribution for a quantum walker to be displaced by $d$ units from its initial position after $k$ steps. For $k$ large, we show that the likelihood is sharply peaked at a displacement determined by the ratio $d/k$, which is correlated with the reshuffling parameter $θ$. We suggest that this `reluctant walker' behaviour provides the framework for maximum likelihood estimation analysis, allowing for robust parameter estimation of $θ$ via return probabilities of closed evolution loops and quantum measurements of the position of quantum walker with`reluctance index' $r=d/k$.
