New Method of Calculating a Multiplication by using the Generalized Bernstein-Vazirani Algorithm

Abstract

We present a new method of more speedily calculating a multiplication by using the generalized Bernstein-Vazirani algorithm and many parallel quantum systems. Given the set of real values { a1, a2, a3, … , aN} and a function g: R→ { 0 , 1 } , we shall determine the following values { g(a1) , g(a2) , g(a3) , … , g(aN) } simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Next, we consider it as a number in binary representation; M1 = (g(a1),g(a2),g(a3),…,g(aN)). By using M parallel quantum systems, we have M numbers in binary representation, simultaneously. The speed of obtaining the M numbers is shown to outperform the classical case by a factor of M. Finally, we calculate the product; M1× M2× ⋯ × MM. The speed of obtaining the product is shown to outperform the classical case by a factor of N × M.