## Generalization of the Bernstein-Vazirani Algorithm Beyond Qubit Systems

**Authors:** Koji Nagata, Tadao Nakamura, Shahrokh Heidari, Ahmed Farouk, Do Ngoc Diep

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.

**Comments:** 7 pages

**Download:** **PDF**

### Submission history

[v1] 2018-09-27 08:18:00

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