论文标题
离散SINC量子状态的特性和用于测量插值的应用
Properties of The Discrete Sinc Quantum State and Applications to Measurement Interpolation
论文作者
论文摘要
提取量子计算的结果是一项艰巨的任务。在许多情况下，量子相估计算法用于数字地编码量子寄存器中的值，该量子寄存器的幅度反映了离散的SINC函数。在标准实现中，该值是通过最频繁的结果近似的，但是，使用其他结果的频率可以提高精度而无需使用其他Qubit。一种现有的方法是使用最大似然估计，该估计使用所有测量结果的频率。我们提供和分析几个替代估计量，其中最好的估计量仅取决于两个最常见的测量结果。基于比率的估计器使用两个最频繁的结果的比率为编码值的小数部分使用封闭形式的表达式。硬币近似估计量取决于以下事实：编码值的小数部分通过Bernoulli过程的参数很好地近似，该参数由最大的两个振幅的幅度表示。我们还提供了离散SINC状态的其他属性，可用于设计其他估计器。
Extracting the outcome of a quantum computation is a difficult task. In many cases, the quantum phase estimation algorithm is used to digitally encode a value in a quantum register whose amplitudes' magnitudes reflect the discrete sinc function. In the standard implementation the value is approximated by the most frequent outcome, however, using the frequencies of other outcomes allows for increased precision without using additional qubits. One existing approach is to use Maximum Likelihood Estimation, which uses the frequencies of all measurement outcomes. We provide and analyze several alternative estimators, the best of which rely on only the two most frequent measurement outcomes. The Ratio-Based Estimator uses a closed form expression for the decimal part of the encoded value using the ratio of the two most frequent outcomes. The Coin Approximation Estimator relies on the fact that the decimal part of the encoded value is very well approximated by the parameter of the Bernoulli process represented by the magnitudes of the largest two amplitudes. We also provide additional properties of the discrete sinc state that could be used to design other estimators.
