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This article focuses on the development of scalable and quantum bit-efficientalgorithms for computing power functions of random quantum states. Twoalgorithms, based on Hadamard testing and Gate Set Tomography, are proposed. Weprovide a comparative analysis of their computational outcomes, accompanied bya meticulous evaluation of inherent errors in the gate set tomography approach.The second algorithm exhibits a significant reduction in the utilization oftwo-qubit gates compared to the first. As an illustration, we apply bothmethods to compute the Von Neumann entropy of randomly generated quantumstates.

Scalable Algorithms for Power Function Calculations of quantum states in NISQ Era