Variational Quantum Algorithm and Its Application on Non-Linear Equations

Quantum algorithms of factoring problem have been paid more and more attention since Shor's algorithm was proposed. Combining the current quantum computer hardware level and integer factorization quantum algorithms, this paper proposes a "classical + quantum" hybrid solution. This scheme first adopts classical methods and corresponding rules in the preprocessing step to simplify the nonlinear equations, which is used to reduce the number of qubits needed for the cost Hamiltonian. Then the variational quantum algorithm is used to find the approximate ground state of the cost Hamiltonian, which encodes the solution of the nonlinear equations. The program was verified on the IBM QX4 quantum machine, and the results showed that this hybrid solution can effectively reduce the quantum resources required to solve the nonlinear equations. (paper)