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Old 2020-01-28, 20:43   #1
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ixfd64's Avatar
Dec 2002

29×79 Posts
Default Quantum trial factoring?

Probably a very dumb question, but can Grover's algorithm be used for trial factoring?
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Old 2020-01-29, 00:19   #2
CRGreathouse's Avatar
Aug 2006

16EA16 Posts

I don't see why not. By Holevo's theorem you'd need at least n qubits to factor an n-bit number, and a factor p could be found in time O(\sqrt{p})=O(\sqrt[4]{N}). (Just search for factors of length 20 bits, 40 bits, 80 bits, ..., n/4 bits, n/2 bits.) It's not as fast as QS or NFS though.

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