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

Abstract

Quantum computing stands at the vanguard of science, focused on exploiting quantum mechanical phenomena like superposition and entanglement. Its goal is to create innovative computational models that address intricate problems beyond classical computers' capabilities. In the Noisy Intermediate-Scale Quantum (NISQ) era, developing algorithms for nonlinear function calculations on density matrices is of paramount importance. This project endeavors to design scalable algorithms for calculating power functions of mixed quantum states. This study introduces two algorithms based on the Hadamard Test and Gate Set Tomography. Additionally, a comparison of their computational outcomes is offered, accompanied by a meticulous assessment of errors inherent in the Gate Set Tomography based approac