# Solving simultaneous multiple chinese remainder theorem on the quantum computer - possible?

Is it possible to solving simultaneous multiple chinese remainder theorem on the quantum computer?

We have $k$ variables. Each variable can take two values.

The question is: can we calculate all possible circuits equations chinese remainder theorem (which may be $2^k$) and reduce to the smallest result on a quantum computer?

I know the question can be very difficult but I wanted to ask.

I hope I have described the problem quite clearly (but maybe there are ambiguities).

For example we have table:

2 3 7 31

A B C D => [RESULT]

0 1 3 4 => 934
0 1 3 27 => 430
0 1 4 4 => 4
0 1 4 27 => 802
0 2 3 4 => 500
0 2 3 27 => 1298
0 2 4 4 => 872
0 2 4 27 => 368


Third line:

0 1 3 4 => 934


means the system of equations:

$x \equiv 0 \pmod 2$

$x \equiv 1 \pmod 3$

$x \equiv 3 \pmod 7$

$x \equiv 4 \pmod {31}$

and solution for this line in CRT (chinese remainder theorem) is 934.

The final result that the algorithm should return (minimum) is 4. This result is in line:

0 1 4 4 => 4


This is just an example - I wanted to show to know what I mean.

Someone may have some idea?

Sorry for the (maybe) difficult question.