离散Sinc量子态的性质及其在测量插值中的应用
Properties of The Discrete Sinc Quantum State and Applications to Measurement Interpolation
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，量子相位估计算法用于对量子寄存器中的值进行数字编码，该值的幅度反映离散sinc函数。在标准实现中，该值由最频繁的结果近似，然而，使用其他结果的频率允许在不使用额外量子位的情况下提高精度。一种现有的方法是使用极大似然估计，其使用所有测量结果的频率。我们提供并分析了几种替代估计，其中最好的只依赖于两个最常见的测量结果。基于比率的估计量使用两个最常见结果的比率对编码值的小数部分使用封闭形式表达式。硬币近似估计依赖于这样的事实，即编码值的小数部分由最大两个幅度的幅度表示的伯努利过程的参数非常好地近似。我们还提供了其他属性的离散sinc状态，可用于设计其他估计。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
