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In some recent papers, e.g. Phys. Rev. Lett. 119, 170501, the problem of gaussian boson sampling is shown to be related to the hafnian of a certain matrix. When applied to the adjacency matrix of a graph, the hafnian gives the number of perfect mathings in that graph.

On the other hand, for some oriented graphs the number of perfect matchings is given by the pfaffian of the antisymmetric adjacency matrix.

Question: Is the pfaffian related to "fermion sampling"?

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  • $\begingroup$ Yes. - - - - - - - $\endgroup$ Jun 9 at 0:06
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    $\begingroup$ @NorbertSchuch, perhaps a reference? $\endgroup$
    – thedude
    Jun 9 at 11:53
  • $\begingroup$ Computing multi-point correlators of fermions in Gaussian states uses Wick's theorem, which says that those correlators are given as the Pfaffian of the two-point correlation matrix. $\endgroup$ Jun 9 at 15:35

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