论文标题
基于矩阵legendre-bregman预测的经典和量子迭代优化算法
Classical and Quantum Iterative Optimization Algorithms Based on Matrix Legendre-Bregman Projections
论文作者
论文摘要
我们考虑了基于它们的Hermitian Matrix空间和设计迭代优化算法定义的Legendre-Bregman预测。 Bregman在Hermitian矩阵上的分歧建立了一般的二元定理，它在证明迭代算法的融合中起着至关重要的作用。我们研究Bregman投影算法的精确和近似。在特殊的kullback-leibler差异的情况下，我们的近似迭代算法产生了最大熵推理的广义迭代缩放量表（GIS）算法的非交通版本和机器学习中的AdaBoost算法。由于Legendre-Bregman的投影是遗传矩阵上的简单矩阵函数，因此适用于算法的每种迭代中的量子算法技术。我们讨论了适用于我们的设置中的几种量子算法设计技术，包括流畅的功能评估技术，两相量子最小发现和NISQ Gibbs状态准备。
We consider Legendre-Bregman projections defined on the Hermitian matrix space and design iterative optimization algorithms based on them. A general duality theorem is established for Bregman divergences on Hermitian matrices, and it plays a crucial role in proving the convergence of the iterative algorithms. We study both exact and approximate Bregman projection algorithms. In the particular case of Kullback-Leibler divergence, our approximate iterative algorithm gives rise to the non-commutative versions of both the generalized iterative scaling (GIS) algorithm for maximum entropy inference and the AdaBoost algorithm in machine learning as special cases. As the Legendre-Bregman projections are simple matrix functions on Hermitian matrices, quantum algorithmic techniques are applicable to achieve potential speedups in each iteration of the algorithm. We discuss several quantum algorithmic design techniques applicable in our setting, including the smooth function evaluation technique, two-phase quantum minimum finding, and NISQ Gibbs state preparation.
