A New Vector Method in Integral Equations

We suggest a method of computing many functions in the same time by using many parallel quantum systems. We use the Bernstein-Vazirani algorithm. Given the set of real values $\{a_1,a_2,a_3,\ldots,a_N\}$, and the function $g:{\bf R}\rightarrow \{0,1\}$, we shall determine the following values $\{g(a_1),g(a_2),g(a_3),\ldots, g(a_N)\}$ simultaneously. By using $M$ parallel quantum systems, we can compute $M$ functions $g^1,g^2,...,g^M$ simultaneously. The speed of determining the $N\times M$ values will be shown to outperform the classical case by a factor of $N$.