A Simple Procedure to Produce Energy Eigenstates of a Hamiltonian by Classically Emulated Quantum Simulation

We propose a simple procedure to produce energy eigenstates of a Hamiltonian with discrete eigenvalues. We use ancilla qubits and quantum entanglement to separate an energy eigenstate from the other energy eigenstates. Our procedure in principle will be applicable for a Hamiltonian with a finite dimensional Hilbert space and with non-generate discrete energy eigenstates. Choosing an initial state properly, we can in principle produce any energy eigenstate of the Hamiltonian.Comment: 7pages, 2 figure