Quantum computing for solving a system of nonlinear equations over gf (q)‎

Abstract EN

Grover’s quantum search algorithm is one of the most widely studied and has produced results in some search applications faster than their classical counterpart by a square-root.

This paper modifies Grover’s algorithm to solve nonlinear equations over Galois Finite field GF (q) in O (√ 2mn ) iteration, while the best classical general solution takes O(2nm) iteration.

The modification is done by using a register for each variable and represent it by n qubits.

The paper also introduces the implementation of the suggested algorithm by using the simulator QCL 5.1.