Quantum computation, quantum information and artificial intelligence have all contributed for the new non-standard learning scheme named Qubit Neural Network (QNN). In this paper, a QNN based on the qubit neuron model is used for real world time series forecasting problem, where one chaotic series and one stock market series were predicted. Experimental results show evidences that the simulated system is able to preserve the relative phase information of neurons quantum states and thus, automatically adjust the forecast’s time shift.