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Boson sampling is a computation that is not doable on classical machines but quite doable on quantum photonic machines.

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(https://www.researchgate.net/figure/Experimental-results-for-3-and-4-boson-sampling-A-B-The-equivalent-3-and-4-boson_fig2_301872712)

The precise generated pattern at the end of the board will take impossibly long to compute/simulate on classical machines.

However, just being a computation that is not doable by classical machines does not seem too rare or special... Classical computers cannot fully simulate the brain of a six-year-old for even a microsecond either.

So are there any practical uses for being able to perform boson sampling, other than doing a computation that classical machines cannot do?

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  • $\begingroup$ related: quantumcomputing.stackexchange.com/a/13234/55. There's not too much of an answer because that's what was known at the time. I don't think the situation changed that much in the meantime though. I'd quickly comment though that "simulating the brain" is a completely different kind of thing. The point of things like boson sampling is that you can "easily" build a relatively small scale device, in a highly controllable situation, which you cannot classically simulate. Point being to show that at least in principle QM can "compute" things hard to reproduce classically $\endgroup$
    – glS ♦
    Commented Nov 4, 2022 at 16:51
  • $\begingroup$ @glS Thank you. I have heard it mentioned that the first milestone for quantum computing is any sample implementation of quantum advantange. As we are presumably already there now, the next milestone is supposedly the simulation of microscopic mechanism of condensed matter physics like superconductivity... Have there been any progress on this? $\endgroup$
    – James
    Commented Nov 4, 2022 at 17:26
  • $\begingroup$ that's a different question. We try to keep each post focused on a specific post, which helps referencing the discussions later on and gives better chances of getting a good answer. If you want to ask a new question you can create a new post about it $\endgroup$
    – glS ♦
    Commented Nov 4, 2022 at 17:31
  • $\begingroup$ @gIS will do. quantumcomputing.stackexchange.com/questions/28828/… $\endgroup$
    – James
    Commented Nov 4, 2022 at 17:37

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There is a number of techniques that use Gaussian boson sampling for approximate solution of some practical problems:

https://iopscience.iop.org/article/10.1088/2058-9565/ab8504/meta

For example, some of them rely on the fact that the probability of observing a particular sample is proportional to the (squared) Hafnian of a particular matrix that specifies the GBS experiment. If the matrix is an adjacency matrix of a graph, then the Hafnian of its matrix is the number of perfect matchings in the corresponding induced subgraph. Denser subgraphs tend to have more perfect matchings. Thus, samples from GBS can be used to search for dense subgraphs in a given graph.

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