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Quantum computing seems to be a very active and promising development area in computer science. However, I am curious as to what impact (if any) quantum computing will have on existing classical numerical techniques, such as CFD?

The following are two quotes from the Wikipedia article on Quantum Computing:

The capacity of a quantum computer to accelerate classical algorithms has rigid limits—upper bounds of quantum computation's complexity. The overwhelming part of classical calculations cannot be accelerated on a quantum computer. A similar fact prevails for particular computational tasks, like the search problem, for which Grover's algorithm is optimal.

and

Solving linear equations:

The Quantum algorithm for linear systems of equations or "HHL Algorithm", named after its discoverers Harrow, Hassidim, and Lloyd, is expected to provide speedup over classical counterparts.

These two quotes seem to be a little at odds. One states that classical calculations cannot be accelerated and the other suggests that there may be some speedup in solving systems of linear equations with quantum algorithms.

So, what would be the effect of quantum computing on CFD? Will there really be no significant impact?

P.S. I'm a little surprised there is no tag for 'quantum computing'.

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  • $\begingroup$ I am (by no means) an expert on the field. By I would say that we are at an early stage of "quantum computing" and we don't have enough information to answer your question. $\endgroup$ – nicoguaro Jul 23 at 13:53
  • $\begingroup$ @nicoguaro ok. So, it seems like we are a long way off from anybody being able to consider implementing and testing specific quantum algorithms to solve things like CFD problems? $\endgroup$ – Time4Tea Jul 23 at 15:25
  • $\begingroup$ Yes, I think so. I even think that we are even far from having a general purpose computer (or equivalent). $\endgroup$ – nicoguaro Jul 23 at 15:27
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There are two major reasons that there is no tag (at least yet) in Computational Science SE:

Currently, the field of quantum computing is just taking off (and nobody really knows if it will eventually fly, or how is this "flying" going to look like). So, as of right now, discussions on how quantum computing can improve computations is strictly theoretical. The quantum computing community is working in (at least) three main directions:

  • theoretical justifications of quantum computing, main theorems, understanding assumptions and limitations
  • hardware implementation (simply building quantum computers, there are lots of unsolved scientific and engineering problems)
  • developing algorithms for existing and new problems, including computational.

I, as a computational scientist, look at the quantum computing world from a distance, but very carefully. In my mind, both this world and I, myself, are not ready to be productive together. This might change in the future, and quantum computing will become a practical branch of computational sciences.

To conclude, it is too early to decide if there will be a significant impact of quantum computing on CFD. It is unlikely to be a major candidate for a "quantum breakthrough".

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  • $\begingroup$ Thanks for your detailed answer, this is very interesting. I wasn't aware of the specific Quantum Computing SE site, but I will have a look at some of the discussion there. $\endgroup$ – Time4Tea Jul 23 at 13:45

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