No. Quantum computers are not a magical technology that makes a machine self-aware simply because it was applied. Regardless of the computing properties of the machine, the software is still needed to make it work. It is the software that provides the functionalities needed for intelligence to emerge from machines.
Quantum computers may be able to make this software and functions run faster. It may be able to do massively parallel computing (using processing power available across the multiverse, which is what makes quantum computing truly interesting) that may not be feasible with traditional computing resources. Regardless, without the software it is just another dumb device.
Also, there is no indication, as of yet, that traditional computers cannot handle the processing requirements for machines to achieve true intelligence. In fact, quite the opposite is true. There is good evidence that our current computing resources are sufficient to achieve this goal.