4 ms·

I do not believe there are any problems known to be solvable by QC, and unsolvable by classical computers. edit: I was trying to be polite, but Scott Aaronson

I do not believe there are any problems known to be solvable by QC, and unsolvable by classical computers. edit: I was trying to be polite, but Scott Aaronson has spilled quite a lot of blog ink denouncing remarks like the parent post as utter nonsense.

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letstryagain 11y ago
You might have misunderstood my comment (or Scott's writings?) Classical computers are limited by what they can compute because the universe has limits. A 10,000 qubit quantum computer can factor fairly large numbers. 10,000 qubits is pretty small, one day hopefully it will fit inside a small room. To factor those same numbers using a classical computer you'd have to make a computer the size of the entire known universe and run that computer until the heat death of the universe. Obviously this is not possible, even in principal. Theoretically any QC computation can be simulated by a classical computer but in our limited universe you quickly run into the wall where the classical computer just becomes too big (bigger than the entire universe) and too slow (slower than the life of the universe).
- dvanduzer 11y ago
  I definitely reread your comment several times and kept stewing on the word "intractable" since I'd seen it used somewhere else to talk about problems in NP-Complete. I assumed if I was misinterpreting what you were saying, it would hinge on that word. Aside from factoring, what kinds of things do we think will meaningfully change if we get general QC? Cryptographers are already preparing for the post-quantum world. Who else needs to be preparing? Everything I think I understand about QC suggests that a practical breakthrough will not cause any changes in society, other than the abandonment of RSA. Am I missing something?
  - phaas 11y ago
    Imagine simulating a human brain. I'm not sure how massive a computer would need to be today to simulate the neurons, but an efficient implementation can be made to be the size of.. Well.. A brain. I could see this causing massive changes in society. An artificial intelligent simulation of a super-smart human, that can be tuned toward a specific problem area and made much more focused and efficient than a purely biological brain could work...
    - dvanduzer 11y ago
      Is there a specific reason a quantum computer would be better at simulating a human brain than a classical computer?
      - drdeca 11y ago
        Well, to simulate the chemistry in the brain, would, I think, involve simulating some quantum mechanical things, which a quantum computer might be better equipped to simulate? Is the argument that I've heard. I don't know how that works when the qubits are being used to deal with other sorts of variables than bits though?
  - nl 11y ago
    It might provide a rapid, general approach to non-convex optimization for neural nets. And that changes everything, probably more than anything since (the iPhone|the internet|computers|penicillin|the industrial revolution|fire) depending on how optimistic you are. It'll change things a lot, anyway. See http://research.microsoft.com/en-us/events/qml/ http://research.microsoft.com/en-us/events/qml/
  - lololomg 11y ago
    Grover's algorithm is a quantum algorithm for searching an unsorted database with N entries in O(N^1/2) time and using O(log N) storage space
  - zodiac 11y ago
    Since you seem to already familiar with integer factoring, isn't factoring large integers something that "solvable by QC, and unsolvable by classical computers"?
- lmm 11y ago
  Not proven. The best currently known algorithms for factoring on a classical computer take asymptotically longer than the best known quantum ones. That doesn't necessarily mean it's a fundamental limit of the universe. More generally we have no proof that BQP =/= P.
nl 11y ago
I do not believe there are any problems known to be solvable by QC, and unsolvable by classical computers. The space between unsolvable by classical computers and solvable practically by classical computers is... significant.
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letstryagain 11y ago

You might have misunderstood my comment (or Scott's writings?) Classical computers are limited by what they can compute because the universe has limits. A 10,000 qubit quantum computer can factor fairly large numbers. 10,000 qubits is pretty small, one day hopefully it will fit inside a small room. To factor those same numbers using a classical computer you'd have to make a computer the size of the entire known universe and run that computer until the heat death of the universe. Obviously this is not possible, even in principal. Theoretically any QC computation can be simulated by a classical computer but in our limited universe you quickly run into the wall where the classical computer just becomes too big (bigger than the entire universe) and too slow (slower than the life of the universe).

dvanduzer 11y ago
I definitely reread your comment several times and kept stewing on the word "intractable" since I'd seen it used somewhere else to talk about problems in NP-Complete. I assumed if I was misinterpreting what you were saying, it would hinge on that word. Aside from factoring, what kinds of things do we think will meaningfully change if we get general QC? Cryptographers are already preparing for the post-quantum world. Who else needs to be preparing? Everything I think I understand about QC suggests that a practical breakthrough will not cause any changes in society, other than the abandonment of RSA. Am I missing something?
- phaas 11y ago
  Imagine simulating a human brain. I'm not sure how massive a computer would need to be today to simulate the neurons, but an efficient implementation can be made to be the size of.. Well.. A brain. I could see this causing massive changes in society. An artificial intelligent simulation of a super-smart human, that can be tuned toward a specific problem area and made much more focused and efficient than a purely biological brain could work...
  - dvanduzer 11y ago
    Is there a specific reason a quantum computer would be better at simulating a human brain than a classical computer?
    - drdeca 11y ago
      Well, to simulate the chemistry in the brain, would, I think, involve simulating some quantum mechanical things, which a quantum computer might be better equipped to simulate? Is the argument that I've heard. I don't know how that works when the qubits are being used to deal with other sorts of variables than bits though?
- nl 11y ago
  It might provide a rapid, general approach to non-convex optimization for neural nets. And that changes everything, probably more than anything since (the iPhone|the internet|computers|penicillin|the industrial revolution|fire) depending on how optimistic you are. It'll change things a lot, anyway. See http://research.microsoft.com/en-us/events/qml/ http://research.microsoft.com/en-us/events/qml/
- lololomg 11y ago
  Grover's algorithm is a quantum algorithm for searching an unsorted database with N entries in O(N^1/2) time and using O(log N) storage space
- zodiac 11y ago
  Since you seem to already familiar with integer factoring, isn't factoring large integers something that "solvable by QC, and unsolvable by classical computers"?
lmm 11y ago
Not proven. The best currently known algorithms for factoring on a classical computer take asymptotically longer than the best known quantum ones. That doesn't necessarily mean it's a fundamental limit of the universe. More generally we have no proof that BQP =/= P.

nl 11y ago

I do not believe there are any problems known to be solvable by QC, and unsolvable by classical computers. The space between unsolvable by classical computers and solvable practically by classical computers is... significant.

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