To tell you the truth, I have never seen quantum theory used to defend belief in an eternal universe. The steady-state theory, also known as the theory of continuous creation, was formerly defended by a minority of physicists in the 50s through the late 20th century, but as far as I know, there is not any influential scientist working today who believes that the universe is eternal. In particular, quantum mechanics has been used by some to at least try to create a theory for the spontaneous creation of the universe. In other words, the quantum world view is used to defend the opposite of the eternal universe. It is not used currently to defend the idea of an eternal universe.
All the information we have at hand through science points toward the conclusion that the universe was created. The laws of thermodynamics predict a heat death for our universe–that by the process of increasing entropy, the entire universe will go cold eventually. This strongly mitigates against the eternal universe! The data also supports that the universe was created by what is known as the “big bang.” This is where cosmology points. As for quantum mechanics, it is not a cosmological theory, but as far as I know, it is not currently used by any important scientist to defend the thoroughly discredited scientific idea of an eternal universe.