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

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}<inline-graphic></inline-graphic> and a function g:R→{0,1}<inline-graphic></inline-graphic>, we shall determine the following values {g(a1),g(a2),g(a3),…,g(aN)}<inline-graphic></inline-graphic> simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N<inline-graphic></inline-graphic>. Next, we consider it as a number in binary representation; <italic>M</italic>1 = (<italic>g</italic>(<italic>a</italic>1),<italic>g</italic>(<italic>a</italic>2),<italic>g</italic>(<italic>a</italic>3),…,<italic>g</italic>(<italic>a</italic><italic>N</italic>)). By using M<inline-graphic></inline-graphic> parallel quantum systems, we have M<inline-graphic></inline-graphic> numbers in binary representation, simultaneously. The speed of obtaining the M<inline-graphic></inline-graphic> numbers is shown to outperform the classical case by a factor of M<inline-graphic></inline-graphic>. Finally, we calculate the product; M1×M2×⋯×MM.<inline-graphic></inline-graphic> The speed of obtaining the product is shown to outperform the classical case by a factor of <italic>N</italic> × <italic>M</italic>. [ABSTRACT FROM AUTHOR]