An Online Algorithm for Maximum-Likelihood Quantum State Tomography
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We propose, to the best of our knowledge, the first online algorithm for maximum-likelihood 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 numerical error of the algorithm is O(√( ( 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).
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