Scalable algorithms for calculating power functions of random quantum states in the noisy intermediate-scale quantum era

This article focuses on the development of scalable and qubit-efficient algorithms for computing power functions of random quantum states. Two algorithms, based on the Hadamard Test and Gate Set Tomography, are proposed. We provide a comparative analysis of their computational outcomes, accompanied by a meticulous evaluation of inherent errors in the Gate Set Tomography approach. The second algorithm exhibits a significant reduction in the utilization of two-qubit gates compared to the first. Consequently, the second algorithm exhibits reduced susceptibility to noise. As an illustration, we apply both methods to compute the von Neumann entropy of randomly generated quantum states. We evaluate the performance of two algorithms by applying noise obtained from actual superconducting systems. The numerical simulation indicates that, in the majority of scenarios, the second algorithm outperforms the first.