
Quantum Factorization of 143 (2011) - lknik
https://arxiv.org/abs/1111.3726
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curuinor
Quantum adiabatic means no proved exponential speedup. I mean, we've factored
stuff with 143 _digits_ with general number field sieve, the only interest is
in the exponential speedup

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est31
Is this true? After reading your comment I looked up what adiabatic quantum
computation is and found this [0]:

> We give an example of an adiabatic quantum algorithm for searching that
> matches the optimal quadratic speedup obtained by Grover’s search algorithm.
> This example demonstrates that the ‘quantum local search’, which is implicit
> in the adiabatic evolution, is truly non-classical in nature from a
> computational viewpoint.

[0]:
[https://people.eecs.berkeley.edu/~vazirani/pubs/adiabatic.pd...](https://people.eecs.berkeley.edu/~vazirani/pubs/adiabatic.pdf)

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bollu
Grover's search offers quadratic (polynomial) speedup, not exponential. As OP
states, adiabatic does not provide for the theoretical possible exponential
speedup, assuming the hypothetical relations of complexity classes P != (NP =
BQP) holds. That is: P and NP are different, so there are "hard exponential
problems" like 3-SAT. Also, NP = BQP, so quantum computers can solve these
hard problems.

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anderskaseorg
We have no evidence that factoring is NP-hard, and some evidence that it
probably isn’t: the best known classical algorithms for factoring are much
faster than those for NP-complete problems. We have no idea whether NP = BQP,
or indeed whether either is contained in the other.

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bollu
Yes, which is why I phrased all of this as "hypothetical relations ..."

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anderskaseorg
This is from 2011.

