  The deterministic quantum computation with one qubit (DQC1) model is a
restricted model of quantum computing able to calculate efficiently the
normalized trace of a unitary matrix. In this work we analyse the quantum
correlations named entanglement, Bell's nonlocality, quantum discord, and
coherence generated by the DQC1 circuit considering only two qubits (auxiliary
and control). For the standard DQC1 model only quantum discord and coherence
appear. By introducing a filter in the circuit we purify the auxiliary qubit
taking it out from the totally mixed state and consequently promoting other
quantum correlations between the qubits, such as entanglement and Bell's
nonlocality. Through the optimization of the purification process we conclude
that even a small purification is enough to generate entanglement and Bell's
nonlocality. We obtain, in average, that applying the purification process
repeatedly by twelve times the auxiliary qubit becomes 99% pure. In this
situation, almost maximally entangled states are achieved, which by its turn,
almost maximally violate the Bell's inequality. This result suggests that with
a simple modification the DQC1 model can be promoted to a universal model of
quantum computing.
