I thought one of the main advantages of QC was that it could (theoretically) solve existing problems that have exponential time complexity with more efficiency. Isn’t the idea that it could make everything faster? Or did I fall for the marketing.
> Isn’t the idea that it could make everything faster?
If that is your understanding, then yes, you have unfortunately fallen for the very mistaken reporting on this.
There are specific algorithms that Quantum Computing can solve faster than regular computers. Some of these algorithms are incredibly important, and a faster solution to them would cause serious changes to the world, namely Shor's algorithm, which would make factoring large numbers much faster. This would effectively break many/most encryption schemes in the world. So it's a big deal!
Nevertheless, this isn't true in general - not every algorithm is known to have such a speedup. (I'm not an expert, I'm not sure if we know that there isn't a general speedup, or think there might be but haven't found it.)
Quadratic speedup, IIRC - a 128-bit key can be found by brute force in (roughly) 2^128 steps by a normal computer, or 2^64 steps by a quantum computer. This applies to all brute force algorithms, so just make your keys and hashes twice as long as you think they should be, and you're good.
This might be true (I'm not that up to date on whether there are symmetrical algorithms that negate the advantage of QC), but most of the internet / world commerce relies on public key crypto.
Huh yeah I guess I need to learn more. My layman’s assumption was that it would help with a lot of NP problems that involved recursion or backtracking algorithm would benefit from it. From some quick googling it seems like they have already designed QC algorithms for traveling salesman etc. Isn’t that sort of meaningful or am I missing something?
I could totally see the argument that they are physically impractical and therefore not likely to be actually used vs parallelizing conventional computers.
Well they are physically impractical now, but they might get practical in the future.
But no, I'm fairly sure that QC in general isn't known to be able to solve NP problems. And since Traveling Salesman is NP complete (iirc), I don't think there's a QC alg to solve traveling salesman in P (otherwise that would imply QC would solve all of NP in P, which I know isn't true). Where did you see indication otherwise?
FWIW, my favorite CS blogger is Scott Aaronson, and the subtitle of his blog has always been: "If you take nothing else from this blog: quantum computers won't
solve hard problems instantly by just trying all solutions in parallel." This reflects the very common misunderstanding of how QC works.
Hah ok point taken. Here’s the paper I found about traveling salesman - looks like a version of Grover’s algorithm so I think that means it provides a speed-up but not polynomial time? Paper is paywalled: https://link.springer.com/article/10.1134/S1063776123080095#....
> Huh yeah I guess I need to learn more. My layman’s assumption was that it would help with a lot of NP problems that involved recursion or backtracking algorithm would benefit from it.
Recursion is more of a property of how you write your algorithm, than of the problem.
Eg Scheme or Haskell as languages have no built-in facilities for iteration, no for-loops, no while-loops; the only thing you get is function calls. (Well, that and exceptions etc.)
However you can built for-loops as libraries in both Scheme and Haskell. But they will be built on top of recursion.
To make matters even more interesting: once you compile to native code, all the recursion (and also all the for-loops and other fancy 'structured programming' constructs) go away, and you are back to jumps and branches as assembly instructions.
None of this changes whether a given class of problems is in P or NP or (almost!) any other complexity class. Just like getting a faster computer doesn't (usually!) change the complexity class of your problems.
> I could totally see the argument that they are physically impractical and therefore not likely to be actually used vs parallelizing conventional computers.
Quantum computers are impractical now. But as far as we can tell, that's "just" an engineering problem.
In the long run one of two things will happen:
- Either engineering improves and we will be able to build good quantum computers (though perhaps still not better than classical computers for the same amount of effort)
- Or, we discover new principles of quantum mechanics.
Basically, quantum mechanics is one of our most successful physical theories, if not the most successful theory. And as far as we understand it, it allows quantum computers to be built.
So either we will eventually manage to built them, or (more excitingly!) that's not possible, and we will discover new physics that explains why. We haven't really discovered new physics like that in a while.
It could make somethings faster, not everything, but so far the number of useful somethings that people have come up with is very small.
A quantum computer is not a general purpose computer than can be programmed in the way we're used to - it's more like an analog computer that is configured rather than programmed. It's only useful if the problem you are trying to solve can be mapped into a configuration of the computer.
The basic idea is that for a certain class of problems, you can have the quantum computer skip certain incorrect paths on the calculation by having their probability amplitudes cancel each other out.
With emphasis very much on '_certain_ class of problems'. It's only a precious few problems quantum computers actually help with as far as we know, even theoretically.
If a problem can be reduced to efficiently sampling from the summation of an exponentially large number of FFT's, then a quantum computer will destroy a classical computer.
If a task can't be efficiently reduced to such a problem, then a QC probably won't ever help at all; the square root time advantage from grover's algorithm is too easily overwhelmed by simple engineering factors.
“We give new evidence that quantum computers—moreover, rudimentary quantum computers
built entirely out of linear-optical elements—cannot be efficiently simulated by classical comput-
ers. In particular, we define a model of computation in which identical photons are generated,
sent through a linear-optical network, then nonadaptively measured to count the number of
photons in each mode. This model is not known or believed to be universal for quantum com-
putation, and indeed, we discuss the prospects for realizing the model using current technology.
On the other hand, we prove that the model is able to solve sampling problems and search
problems that are classically intractable under plausible assumptions.”
