
A low-resource quantum factoring algorithm [pdf] - sigil
https://eprint.iacr.org/2017/352.pdf
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swordswinger12
From the abstract: "The new time complexity is asymptotically worse than
Shor’s algorithm, but the qubit requirements are asymptotically better, so it
may be possible to physically implement it sooner."

This is a nice result that shows how to speed up the best-known classical
factorization algorithm using a quantum algorithm for one of the steps.
Importantly, it does it using _asymptotically fewer_ qubits than Shor's
algorithm requires. However, the overall algorithm in the paper is still
subexponential, not polynomial like Shor.

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cromwellian
So to factor a 2048-bit number, Shor's algorithm would need about 4000 qubits,
and this algorithm would need about 126 qubits (log(2^2048)^(2/3)). I wonder
which would finish first: waiting for a 4000-qubit computer, and then
factoring in exponentially faster time, or waiting for a 126-bit qubit
computer, and then waiting for the sub-exponential algorithm to complete? :)

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SAI_Peregrinus
Well, since the difficulty of constructing (general purpose) quantum computers
seems to be exponential in the number of bits, waiting for a 4k-bit one is
likely the slower option.

