First, we review the Bernstein-Vazirani algorithm for determining a bit string. Next, we discuss the generalized Bernstein-Vazirani algorithm for determining a natural number string. Finally, we discuss the generalized Bernstein-Vazirani algorithm for determining an integer string. All of the generalized algorithms presented here have the following structure. Given the set of real values $\{a_1,a_2,a_3,\ldots,a_N\}$ and a special function $g$ , we determine $N$ values of the function $g(a_1),g(a_2),g(a_3),\ldots, g(a_N)$ simultaneously. The speed of determining the strings is shown to outperform the best classical case by a factor of $N$ in every case.First, we review the Bernstein-Vazirani algorithm for determining a bit string. Next, we discuss the generalized Bernstein-Vazirani algorithm for determining a natural number string. Finally, we discuss the generalized Bernstein-Vazirani algorithm for determining an integer string. All of the generalized algorithms presented here have the following structure. Given the set of real values $\{a_1,a_2,a_3,\ldots,a_N\}$ and a special function $g$, we determine $N$ values of the function $g(a_1),g(a_2),g(a_3),\ldots, g(a_N)$ simultaneously. The speed of determining the strings is shown to outperform the best classical case by a factor of $N$ in every case.

Sep 1, 20180 citations

Generalization of Deutsch’s Algorithm

Koji Nagata, Tadao Nakamura

International Journal of Theoretical PhysicsJun 29, 20207 citations

\{a_1,a_2,a_3,\ldots,a_N\}

and a special function

g

, we determine

N

values of the function

g(a_1),g(a_2),g(a_3),\ldots, g(a_N)

simultaneously. The speed of determining the strings is shown to outperform the best classical case by a factor of

N

in every case.