  Presented here is a matrix inversion method utilizing quantum searching
algorithm. In this method, huge Hilbert space as a whole spanned by myriad of
eigen states is searched and evaluated efficiently by sequential reduction in
dimension one by one. Total iteration steps required for search are
proportional to the number of unknown variables. Our method could solve very
large linear equations with sufficiently high probability faster than any
existing classical algorithms, which roughly depends on the cube of unknown
variables.
