It's (very) early days yet, so we just haven't got to the point where they're properly useful - there are scientists at D-Wave doing actual science (completely unrelated to quantum computing) but we're a fair bit away from reaching the point where a quantum computer is unquestionably faster than any classical computer (known as quantum computational supremacy, although many people don't like that name)

@Blue indeed, in the HHL paper they use the notation $|\tilde{\lambda}_k\rangle$, to express the fact that the output of the QPE gives you an approximation to the (state corresponding to the) true eigenvalue. I think you have to look at the error analysis to see the scaling in terms of number of qubits for a given target precision

@Mithrandir24601 oh the people here are doing research only ?

@Blue Wait, did someone mention non-Hermitian?

@Blue Where?

@O.Rares At the companies, practically everything is research - there are people making programming languages but that's also pretty much research. If you wanted to create an app, that would pretty much be research as well because no-one's (to my knowledge) done so before, so you'd probably need to come up with new ways/algorithms for things to work well. On this site, we do have researchers, but not everyone is a researcher

@Blue Thanks!! :D

Oh yeah, I've seen that before :P

:(

I got super excited there for a moment

@Blue Yep, although a rather neat one

There was a preprint put on arXiv a week or so ago about making a quantum PT-symmetric photonic system would require adding additional thermal noise, which I was a bit sad about though

@Mithrandir24601 thanks ,I think that I should wait a while in order to study this in a way that can be a safe bet for me

Good look everyone

@O.Rares It depends on what you find interesting. Quantum cryptography is something that companies are now beginning to sell...

@Blue Also this: researchers research because it's interesting

@Mithrandir24601 are you looking for ways to implement/simulate non-hermitian matrices with photonics?

what if the quantum computers will fail ? We are close to 6 nm at processors

Then we'll do something else?

@glS Well, I'd be looking for better ways to do so...

so people know what to expect

If it's successful, people will keep doing it. If it's not, people will do something else.

@Blue I will remember this quote in future

@O.Rares There's an interesting thing here in that people researching spintronics could (are!) finding applications for classical computing due to the small size of processors

techtimes.com/articles/132350/20160211/…

@Blue Scott Aaronson often says that if it turned out that quantum computation cannot do better than classical computation, than that would be even more interesting than if it can

@Mithrandir24601 interesting that Intel and AMD don't complain about patent theft

@Blue a naive guess would be $\sim\log_2 N$ for the eigenvector register, plus that number you gave from N&C, plus 1 for the ancillae. The $\epsilon$ has to be chosen beforehand and determines the precision of the result

I bounced this story (well, a story like this) off of the MSE chat and wanted to get a reaction from here as well

Every week, two people (Alice and Bob) each pick one of three different shows (1,2,3) to watch on TV. They have similar enough tastes that: (1) if they watch the same show, then they'll both either dislike the show (+1) or both dislike the show (-1); if they were to swap which shows they watch, they'd get the same outcomes.

@Mithrandir24601 as in you're already doing it/have done it somehow? (I think I've already asked this question but don't remember the answer)

(So if A likes show 1 and B dislikes show 2, then B would have liked show 1 and A would have disliked show 2.)

In addition, none of the three shows are particularly good and so they're just as likely as not to enjoy a given show

@Blue that looks correct. So $7\log_2 N+1$. For $N=4$ you get $15$. Just what you need to improve on the state of the art of $N=2$ right?

From the above, the conditional probabilities must satisfy:

P(++|11) = P(++|22) = P(++|33) = P(--|11) = P(--|22) = P(--|33) = 1/2,
P(+-|11) = P(+-|22) = P(+-|33) = P(-+|11) = P(-+|22) = P(-+|33) = 0,
P(++|12)  = 1/2 - P(-+|12) = 1/2 - P(-+|12)  = P(--|12),

bah, last line was incomplete

P(++|12)  = 1/2 - P(-+|12) = 1/2 - P(+-|12)  = P(--|12) = P(++|21) = ...,
P(++|13)  = 1/2 - P(-+|13) = 1/2 - P(+-|13)  = P(--|13) = P(++|31) = ...,
P(++|23)  = 1/2 - P(-+|23) = 1/2 - P(+-|23)  = P(--|23) = P(++|32) = ...,

With the upshot being that this scenario is dictated entirely by the probabilities P(++|12), P(++|13), P(++|23)

The question: Given a particular choice of those three numbers, does this scenario make sense?

As an example, suppose P(++|12) = P(++|13) = P(++|23)=p. How small can p be?

(The surprise is that this is basically a Bell inequality in disguise.)

@glS How to answer this? In a fashion, yes

@Mithrandir24601 as in, it's not published yet? =)

@glS You would be right on that :P

I understand, no worries!

It is on my poster, but that poster still hasn't been outside of Bristol yet

Oh! My secondary supervisor might have mentioned it at the PT-symmetry conference

"I will present experimental results for multi-particle correlations and quantum information across the PT transition, obtained by using a quantum photonic chip" :) Yay! It's now been at a conference

(although most/the vast majority of it wasn't my work, to be fair)

(If anyone is curious, I'll explain my above rambling. But I'm not sure how interesting I made it soooo yeah)

@Mithrandir24601 haha congratulations. The abstract looks interesting

@Semiclassical sorry, that looks interesting but I don't have time atm to read it carefully (though it looks a lot like the stuff you get in quantum contextuality). Will read better later

mmkay

@Blue that still sounds like a lot. I don't think they can "easily" simulate that many qubits without using tricks

There's two punchlines, one of which I think I fully comprehend and one which I'm not sure I do.

So I'm not without an ulterior motive.