It is about 30 years since the advent of quantum information and quantum computation theory, in which promising improvements could be acheived. Quantum algorithms seem to be improving up with the speed of the everyday, and scientists believe that one day, even quantum computers will be replaced or used with home computers. In this thesis, we suggest three quantum algorithms for logestic regression, sparse matrix trace and sparse matrix determinants respectively. Our suggested quantum algorithms have speedup versus algorithms. Additionally, we suggest few applications for above quantum algorithms.We begin by reviewing and introducing the sciences of computation and physics. Then, given the analytic properties of quantum mechanics, we have given definitions and applications for quantum computing, and then quantum algorithms that are relevant to the purpose of this research. Finally, the ideas and calculations of this research are examined in the last two chapters.