Abstract
Diophantine equations are multivariate equations, usually polynomial, in
which only integer solutions are admitted. A brute force method for finding
solutions would be to systematically substitute possible integer solutions and
check for equality.
Grover's algorithm is a quantum search algorithm which can find marked
indices in a list very efficiently. By treating the indices as the integer
variables in the diophantine equation, Grover's algorithm can be used to find
solutions in brute force way more efficiently than classical methods. We
present an example for the simplest possible diophantine equation.