Does the Universe have a Hard Drive?

We discuss an apparent information paradox that arises in a materialist's description of the Universe if we assume that the Universe is 100% quantum. We discuss possible ways out of the paradox, including that Laws of Nature are not purely deterministic, or that gravity is classical. Our observation of the paradox stems from an interdisciplinary thought process whereby the Universe can be viewed as a "quantum computer". Our presentation is intentionally nontechnical to make it accessible to as wide a readership base as possible.