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factoring large integers into primes (shor's algorithm). that and grover's search promise to provide ways to crack a lot of encryption.

also quantum computing should improve both classical and quantum physical simulations.



The other side of Shor's algorithm is that you can use it to solve discrete logarithm (which additionally breaks elliptic curve crypto; factoring breaks RSA).

I don't agree that Grover's algorithm is as fundamental in breaking encryption, since it "only" yields a quadratic speed-up. You'd have similar effective security as in the pre-quantum world by doubling the key length; you could do this by, say, switching to AES-256 instead of AES-128. Meanwhile, switching from RSA-2048 to RSA-4096 only helps if it means the problem size now exceeds the size of the biggest quantum computers.




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