It’s Time to Learn about Quantum Computing
wired.com
wired.com
If you know you linear algebra well, learning quantum mechanics is not so complicated, see the book preview here: https://minireference.com/static/excerpts/noBSguide2LA_previ...
But practical problems don't need to be so large; approximately optimal solutions might save 90% of the money of optimal solutions and very valuable; real problems commonly are not much like the worst case problems; and we long had lots of methods for combinatorial optimization that do quite well in practice.
Point: If practical problems in combinatorial optimization are of interest, then bring them forward -- they've been coming forward mostly only rarely. Else, let's find other reasons for pressing forward with quantum computers.
> There is a common misconception that quantum computers can solve NP-complete problems in polynomial time. That is not known to be true, and is generally suspected to be false.[120]
The citation is from 1997, but I seem to remember that someone came up with a proof sometime in the last decade...? Probably just my faulty memory rather than the Wikipedia being out of date.
See https://en.wikipedia.org/wiki/BQP for the relation of BQP to other complexity classes.
(I was actually looking at the BQP page,, but then realized that I know far less about the Q classes than I should and found the more general "quantum computing" page where my citation is from.)
I'll assume that the cubits will be able to do total enumeration right away!
Now, while we are waiting on that, if there are some problems in combinatorial optimization to solve, trot them out and we will see. Maybe for some of the problems, current techniques can make big bucks.
"Is the input empty" is in the class NP. You mean these problems are NP-complete. (This means "In NP, and all other problems in NP can be reduced to them in polynomial time.")
> If practical problems in combinatorial optimization are of interest, then bring them forward -- they've been coming forward mostly only rarely.
This is total nonsense. Training a neural network is combinatorial optimisation, proving mathematical theorems is NP-complete (when max proof-length is specified in unary), and there are loads of integer programs running all over the place that we'd love to solve significantly faster.
Sure, maybe you don't always need to get to optimality, but every bit helps, and often approximate methods just aren't good enough.
(As the sibling comment points out, though, none of this is really germane to a discussion of quantum computers.)
> there are loads of integer programs running all over the place that we'd love to solve significantly faster.
Some years ago I had a good background in optimization including integer programming and had some successes. But slowly I had to conclude that actually the world had decided that such optimization was just not worth the bother. So, I never saw "loads".
Once I talked to a guy, and we considered airline scheduling (I got started in that when I was Director of Operations Research at FedEx). His remark was that optimization was no good because the schedules it gave were "too tight". That's like a kid who likes chocolate cake saying that he doesn't want to eat any of his orange flavored birthday cake because it is too big. Having the optimization put, say, five minutes of slack at each stop in the schedule is the easiest thing in the subject.
Mostly people in business just do NOT want anything technical they don't understand. So, as soon as mention, say, Lagrangian relaxation, they want nothing to do with integer programming. Or if such a project flops, then they have a failure on their record. If the project is successful, maybe the integer programming guy is a threat.
> optimization was no good because the schedules it gave were "too tight".
This matches fairly well with my experience -- getting a good objective function can be half the battle. A lot of people don't know what they want well enough to tell you.
> Mostly people in business just do NOT want anything technical
Well, in competitive markets it'll eventually be "do or die", and for common enough problems it doesn't need to be done in-house. I agree that businesses are (typically) very conservative about this sort of thing, but if there's value to be had by wringing efficiencies out of operations, Uber and Amazon will do it.
> So how do they work? You may have heard that the normal rules of reality don’t always apply in the world of quantum mechanics. A phenomenon known as a quantum superposition allows things to kinda, sorta, be in two places at once, for example. In a quantum computer, that means bits of data can be more than just 1 or 0, as they are in a conventional computer; they can also be something like both at the same time.
When data is encoded into effects like those, some normal limitations on conventional computers fall away. That allows a quantum computer to be much faster on certain tricky problems. Want a full PhD, or third-grade, explanation? Watch the video above.