4 ms·

One of the collections of current practical problems frequently and continually mentioned as big reasons for developing quantum computers is combinatorial optim

One of the collections of current practical problems frequently and continually mentioned as big reasons for developing quantum computers is combinatorial optimization. Right, these problems are commonly in the class NP, and that means that so far, as problem size grows, the guaranteed sufficiently large time and or space on a current, classic digital computer to get optimal solutions of worst case problems grows like an exponential in the problem size. 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.

lomnakkus 8y ago
Per Wikipedia isn't not actually known whether quantum computers will be able to solve NP-complete problems in polynomial time: > 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 Probably just my faulty memory rather than the Wikipedia being out of date.
- graycat 8y ago
  Too much detail for me!!! 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.
- abdullahkhalids 8y ago
  There is no known proof of separation between BQP and NP. See https://en.wikipedia.org/wiki/BQP https://en.wikipedia.org/wiki/BQP for the relation of BQP to other complexity classes.
  - lomnakkus 8y ago
    Ah, thanks. (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.)
repsilat 8y ago
> these problems are commonly in the class NP "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.)
- graycat 8y ago
  Sorry about saying NP instead of NP-complete -- I've been doing other things for a long time and typed too quickly. > 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.
  - repsilat 8y ago
    Thanks for writing back, sorry if my tone wasn't great before. > 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.

lomnakkus 8y ago

Per Wikipedia isn't not actually known whether quantum computers will be able to solve NP-complete problems in polynomial time: > 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.

graycat 8y ago
Too much detail for me!!! 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.
abdullahkhalids 8y ago
There is no known proof of separation between BQP and NP. See https://en.wikipedia.org/wiki/BQP https://en.wikipedia.org/wiki/BQP for the relation of BQP to other complexity classes.
- lomnakkus 8y ago
  Ah, thanks. (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.)

repsilat 8y ago

> these problems are commonly in the class NP "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.)

graycat 8y ago
Sorry about saying NP instead of NP-complete -- I've been doing other things for a long time and typed too quickly. > 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.
- repsilat 8y ago
  Thanks for writing back, sorry if my tone wasn't great before. > 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.