Simulating a quantum circuit for solving, two variable modulo function using discrete logarithm problem.
Discrete log problem - Give a prime $p$, a primitive root $g$, and
$h \not\equiv 0(modp)$ (which means $gcd(h,p)=1)$.
Find $x$ so that $g^x \equiv h(modp)$ or $Dis\log_{g}h \equiv x$.
From Neilsen Chuang
textbook we solve a two variable modulo function $f(x) \equiv a^{sx_{1} + x_{2}}(modN)$ where
$a^{r} \equiv 1(modN)$, using discrete logarithm by taking $a^{s} = b$
and solving $s$ by $a^{r}(modN)$ and $b^{r}(modN)$ by modular exponentiation.
The code is designed specifically for $a=4$, $b=13$ and $N=17$.
The cicuit is
The result gave out $s=35$ and more qubit are required
for efficiently finding the value of s. These kind of
problem can be solved efficiently only if there is a
mechanism or a set of steps to find oracle for any
value of multiplication modulo N.