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> A quantum computer AFAIK can't solve any problems a normal computer couldn't solve, but it is a lot more efficient for some of them. Technically correct, but

by jonknee 10y ago

> A quantum computer AFAIK can't solve any problems a normal computer couldn't solve, but it is a lot more efficient for some of them. Technically correct, but some of the problems we want quantum computers to solve are currently infeasible by conventional means because of speed. Factorization for example, that's why public key encryption works (we can't brute force it), but a quantum computer could.

weinzierl 10y ago
I didn't down vote you but here are a few remarks about your comment: >> [..] but it is a lot more efficient for some of them. > Technically correct Not quite. We know algorithms which have better time complexity on a quantum than any known classical algorithm that solves the same problem. Shor's algorithm is an example. We are not sure if a classical algorithm with the same time complexity exists. >Factorization for example, that's why public key encryption works (we can't brute force it), but a quantum computer could. Most (all?) modern public key algorithms are not based on the integer factorization problem.
- cyphar 10y ago
  > >Factorization for example, that's why public key encryption works (we can't brute force it), but a quantum computer could. > Most (all?) modern public key algorithms are not based on the integer factorization problem. There are analogues for Shor's algorithm for the discrete logarithm and other similar problems.
  - PeCaN 10y ago
    Shor's algorithm covers discrete logarithm also. But most modern asymmetric algorithms are based on elliptic curves and other problems that quantum computers don't help with.
    - serendipitous 10y ago
      The ECC algorithms used today rely on the "Elliptic Curve Discrete Logarithm Problem" and are very much vulnerable to (a version of) Shor's algorithm. Some would even say they are more vulnerable than RSA due to the much smaller key sizes (requiring less qubits).

by jonknee 10y ago

weinzierl 10y ago

I didn't down vote you but here are a few remarks about your comment: >> [..] but it is a lot more efficient for some of them. > Technically correct Not quite. We know algorithms which have better time complexity on a quantum than any known classical algorithm that solves the same problem. Shor's algorithm is an example. We are not sure if a classical algorithm with the same time complexity exists. >Factorization for example, that's why public key encryption works (we can't brute force it), but a quantum computer could. Most (all?) modern public key algorithms are not based on the integer factorization problem.

cyphar 10y ago
> >Factorization for example, that's why public key encryption works (we can't brute force it), but a quantum computer could. > Most (all?) modern public key algorithms are not based on the integer factorization problem. There are analogues for Shor's algorithm for the discrete logarithm and other similar problems.
- PeCaN 10y ago
  Shor's algorithm covers discrete logarithm also. But most modern asymmetric algorithms are based on elliptic curves and other problems that quantum computers don't help with.
  - serendipitous 10y ago
    The ECC algorithms used today rely on the "Elliptic Curve Discrete Logarithm Problem" and are very much vulnerable to (a version of) Shor's algorithm. Some would even say they are more vulnerable than RSA due to the much smaller key sizes (requiring less qubits).