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Quantum state tomography (QST) is one of the key steps in determining the state of the quantum system, which is essential for understanding and controlling it. With statistical data from measurements and Positive Operator-Valued Measures (POVMs), the goal of QST is to find a density operator that best fits the measurement data. Several optimization-based methods have been proposed for QST, and one of the most successful approaches is based on Accelerated Gradient Descent (AGD) with fixed step length. While AGD with fixed step size is easy to implement, it is computationally inefficient when the computational time required to calculate the gradient is high. In this paper, we propose a new optimal method for step-length adaptation, which results in a much faster version of AGD for QST. Numerical results confirm that the proposed method is much more time-efficient than other similar methods due to the optimized step size. [ABSTRACT FROM AUTHOR]