A quantum computer can solve problems even without being switched on.
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References
Mitchison,G. & Jozsa, R. Counterfactual computation. Proceedings of the Royal Society London A 457,1175-1193(2001).
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Ball, P. The ultimate no-brainer. Nature (2001). https://doi.org/10.1038/news010503-6
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DOI: https://doi.org/10.1038/news010503-6