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tl;dr- Quantum computers can't really help us to simulate the whole universe as the universe is likely vastly more complex than even quantum mechanics can capture, plus we can't even begin to guess how big it is or many other basic fundamental features. In short, simulating the whole universe is beyond sci-fi. We can't really simulate the entire universe, ...

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It seems this problem is open. Watrous [J. Comp. Sys. Sci. 59, (pp. 281-326), 1999] proved that any space $s$ bounded quantum Turing Machine (for space constructible $s(n)>\Omega(\log n)$) can be simulated by deterministic Turing machine with $O(s^2)$ space. With the assumption $\mathsf{P \neq SC}$ (where $\mathsf{SC \subseteq P}$ is defined as ...

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It's not so much a matter of big data, but that of saving data. Quantum storage is still (much like the rest of the field) in its infancy. (Take what I write with a grain of salt. It's likely to change rapidly.) There are a few theories on how quantum computers might be able to hold "memory". One of these is using nuclear spin. E.g. using long-lived ...

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This doesn't exactly answer your question, but it may aid you in understanding the problem and possibly the solution: In their paper "Breaking the 49-Qubit Barrier in the Simulation of Quantum Circuits" (arXiv:1710.05867), the authors describe simulating a 49-qubit and a 56-qubit quantum computer. According to the paper, they required 4.5 Terrabytes of RAM ...

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