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I am a complete noob w.r.t. Quantum computing, but how exactly does Quantum computing help with Computational Fluid Dynamics? Isn't CFD an issue of efficient pa

I am a complete noob w.r.t. Quantum computing, but how exactly does Quantum computing help with Computational Fluid Dynamics? Isn't CFD an issue of efficient parallel computation and scaling of computing resources?

simiones 3y ago
There are certain classes of problems where (theoretical) QCs show an exponential speed-up over classical computers. These generally have to do with certain statistical properties of (theoretical) qbits (mainly related to the stronger-than-classical correlations between measurements on entangled particles, as far as I understand). Note that I'm only saying theoretical QCs since no actually realized QC has been complex enough to show these speed-ups in a way that convinces everyone (though Google's device has shown a speed-up that is hard to argue with). However, it's important to note that any proof that physically-realized QCs wouldn't actually show these speed-ups would be a monumental discovery in quantum mechanics, as it would represent proof that quantum mechanics is wrong.
- bawolff 3y ago
  Yeah, but is this one of them? The press release is missing what the (theoretical) big-oh would be or any other discussion of what the expected performance gain would be, even in the best case.
  - xmcqdpt2 3y ago
    Likely this is an application of the Quantum Fourier Transform, which is O(n^2) where the classical analogue would be O(2^n) for n qubits. It's important to note as a caveat that no currently existing quantum computers are anywhere near good enough to implement such a deep circuit.
    - bawolff 3y ago
      Is there a reason to assume that beyond QFT being famous?
      - xmcqdpt2 3y ago
        Fourier methods are pretty common in PDEs and the QFT is the core ingredient of many quantum computing algos, such as the quantum phase estimation algorithm used to find eigenvectors (such as modes of wave equations) or the HHL algorithm used to solve linear systems of equations (for example linearized PDE). Let's check the literature though, https://www.nature.com/articles/s41534-020-00291-0 https://www.nature.com/articles/s41534-020-00291-0 So apparently there are also quantum lattice gas models used for this, I know very little about those, but all the other methods are QFT based.

simiones 3y ago

There are certain classes of problems where (theoretical) QCs show an exponential speed-up over classical computers. These generally have to do with certain statistical properties of (theoretical) qbits (mainly related to the stronger-than-classical correlations between measurements on entangled particles, as far as I understand). Note that I'm only saying theoretical QCs since no actually realized QC has been complex enough to show these speed-ups in a way that convinces everyone (though Google's device has shown a speed-up that is hard to argue with). However, it's important to note that any proof that physically-realized QCs wouldn't actually show these speed-ups would be a monumental discovery in quantum mechanics, as it would represent proof that quantum mechanics is wrong.

bawolff 3y ago
Yeah, but is this one of them? The press release is missing what the (theoretical) big-oh would be or any other discussion of what the expected performance gain would be, even in the best case.
- xmcqdpt2 3y ago
  Likely this is an application of the Quantum Fourier Transform, which is O(n^2) where the classical analogue would be O(2^n) for n qubits. It's important to note as a caveat that no currently existing quantum computers are anywhere near good enough to implement such a deep circuit.
  - bawolff 3y ago
    Is there a reason to assume that beyond QFT being famous?
    - xmcqdpt2 3y ago
      Fourier methods are pretty common in PDEs and the QFT is the core ingredient of many quantum computing algos, such as the quantum phase estimation algorithm used to find eigenvectors (such as modes of wave equations) or the HHL algorithm used to solve linear systems of equations (for example linearized PDE). Let's check the literature though, https://www.nature.com/articles/s41534-020-00291-0 https://www.nature.com/articles/s41534-020-00291-0 So apparently there are also quantum lattice gas models used for this, I know very little about those, but all the other methods are QFT based.