We boldly hypothesize that if we build a sufficiently large quantum computer and try to factor a large integer with it, we will find it doesn't work due to a previously unknown fundamental physical limitation of the universe. Therefore, we should put LHC levels of effort (and funding) toward quantum computing to probe the deepest secrets of the universe. (This may already be happening for other reasons, commercial intererst in quantum computing.)
The intuition is that Shor's algorithm seems too good to be true. Maybe we're living in a simulation, and large quantum computers are annoying to simulate so the universe is designed to make them not possible.
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