  In mathematical aspect, we introduce quantum algorithm and the mathematical
structure of quantum computer. Quantum algorithm is expressed by linear algebra
on a finite dimensional complex inner product space. The mathematical
formulations of quantum mechanics had been established in around 1930, by von
Neumann. The formulation uses functional analysis, linear algebra and
probability theory. The knowledge of the mathematical formulation of QM is
enough quantum mechanical knowledge for approaching to quantum algorithm and it
might be efficient way for mathematicians that starting with mathematical
formulations of QM. We explain the mathematical formulations of quantum
mechanics briefly, quantum bits, quantum gates, quantum discrete Fourier
transformation, Deutsch's algorithm and Shor's algorithm.
