论文标题
贝叶斯阶段估计，适应性网格细化
Bayesian phase estimation with adaptive grid refinement
论文作者
论文摘要
我们介绍了一种基于自适应网格细化方法的新型贝叶斯相位估计技术。该方法会自动选择使用网格细节和细胞合并策略进行准确相位估计所需的数字粒子，以使每个步骤所需的颗粒总数最小。所提出的方法为基于传统采样的顺序蒙特卡洛方法提供了强大的替代方法，该方法在某些情况下（例如后验分布是双峰时）往往会失败。我们还将基于网格的方法和基于抽样的方法与混合粒子过滤器相结合，基于网格的方法可用于估计剩余的一组参数集，基于网格的参数集和基于LIU-WEST（LW）SMC。主要峰度分析可用于决定用于网格细化方法和基于抽样方法的参数的选择。我们提供了数字结果，将提出的网格细化方法与基于LIU-WEST重新采样的SMC的性能进行比较。数值结果表明，所提出的方法对于量子相估计非常有前途。它可以很容易地适应哈密顿学习，这是一种非常有用的技术，用于估计哈密顿量未知参数和表征未知的量子设备。
We introduce a novel Bayesian phase estimation technique based on adaptive grid refinement method. This method automatically chooses the number particles needed for accurate phase estimation using grid refinement and cell merging strategies such that the total number of particles needed at each step is minimal. The proposed method provides a powerful alternative to traditional sampling based sequential Monte Carlo method which tend to fail in certain instances such as when the posterior distribution is bimodal. We also combine grid based and sampling based methods as hybrid particle filter where grid based method can be used to estimate a small but dominant set of parameters and Liu-West (LW) based SMC for the remaining set of parameters. Principal kurtosis analysis can be used to decide the choice of parameters for grid refinement method and for sampling based methods. We provide numerical results comparing the performance of the proposed grid refinement method with Liu-West resampling based SMC. Numerical results suggest that the proposed method is quite promising for quantum phase estimation. It can be easily adapted to Hamiltonian learning which is a very useful technique for estimating unknown parameters of a Hamiltonian and for characterizing unknown quantum devices.
