417 karma · joined September 18, 2011
http://dabacon.org/
Also highly recommend his Boojums.
As a grad student in quantum computing we used to have a game where we would race to see who could be the first one to spot the flaw in a paper that claimed an efficient quantum polynomial time algorithm for NP-complete problems.
My bet after a few minutes looking at the paper is Eq. 16. Eq. 15 is computing the clauses with a traditional clause oracle \sum_x |x>|C(x)> where C(x) is a vector of the clauses evaluated on the input x. Eq. 16 claims that one can ignore the first register and this becomes \sum_x |C(x)>. That's not correct: the system is entangled across those two registers, and the partial portion of one of those systems is a mixed state. In particular there is no coherence between the |C(x)> states. The next step relies crucially on this property.
(yes I've read the book and mostly agree with that review)
Quantum simulations. Sampling from solutions to linear equations. Shit we haven't discovered yet (you be shocked at how little research there is in quantum computing looking for new algorithms)
Some problems 1) the procedure appears to require 100 percent detection of photons (there is no analysis of this in the paper). This is not practical and ends up being a source of decoherence (the very thing this paper is supposed to avoid) 2) the scheme depends for its gates and construction of a graph state (a kind of resource quantum state) on precise settings of polarized beam splitters, something which will certainly have errors and hence...decoherence again. 3) the author shows how to create a graph state but makes no mention of why this state will persist. Why won't it deco here while waiting for the necessarily adaptive measurement?
"According to another top official also involved with the program, the NSA made an enormous breakthrough several years ago in its ability to cryptanalyze, or break, unfathomably complex encryption systems employed by not only governments around the world but also many average computer users in the US."
The article insinuates that it's AES (or something closely related.) That would be pretty amazing.
I'd also note that while this is a very cool experiment, the fact that it was performed using a scanning tunneling microscope means it's not exactly a practical device :) But as a proof of principle of storing a bit in a few number of atoms, this is a very neat result.
An interesting example of how one discovers a quantum algorithm is the story of the NAND tree algorithm (See http://www.scottaaronson.com/blog/?p=207 for a nice explanation.) Quite literally the quantum algorithm was discovered by thinking about interference of particles hoping around, combined with physicists uncanny ability to calculate scattering cross sections. Crazy stuff!