We propose, to the best of our knowledge, the first online algorithm to compute the maximum-likelihood estimate in quantum state tomography. Suppose the quantum state to be estimated corresponds to a $D$-by-$D$ density matrix. The per-iteration computational complexity of the algorithm is $O ( D ^ 3 )$, independent of the data size. The expected optimization error of the algorithm is $O(\sqrt{ ( 1 / T ) D \log D })$, where $T$ denotes the number of iterations. The algorithm can be viewed as a quantum extension of Soft-Bayes, a recent algorithm for online portfolio selection (Orseau et al. Soft-Bayes: Prod for mixtures of experts with log-loss. Int. Conf. Algorithmic Learning Theory. 2017).
翻译：据我们所知,我们建议使用第一个在线算法来计算量子状态摄影中最大似值估计值。 假设所估算的量子状态与美元乘以美元密度矩阵相对应。 算法的人均计算复杂性为$O( D $ 3), 与数据大小无关。 算法的预期优化误差是$O( sqrt { ( 1/ T) D log D } $( $T), 表示迭代数。 算法可以被视为Soft- Bayes的量级扩展, 这是最近在线组合选择的算法( Orseau et al. Soft- Bayes: Prod for command withlog- loss. Int. Conf. Algorthmic Learning Theory. 201717 ) 。
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