The closest thing I know is the computer vision problem, in which an image is de-blurred and/or de-noised by quadratizing a quartic problem into a quadratic optimization problem (QUBO) and then the QUBO is solved. However it seems that deep neural networks solve this computer vision problem much more efficiently. Are there any cases where quadratization is an essential component of a state-of-the-art algorithm for a real-world problem?
Added: I thank the user named Rob for answering my question when no one else did, but I am still looking for an answer. The copying and pasting of those abstracts from papers that I am very familiar with, was not really what I was looking for (in fact I am an author on one of those papers!). The statement "Quadratization has been used in pseudo-Boolean optimization (Implementation of QPBO (C++)) and unconstrained binary polynomial optimization problems" is not really true, because QPBO happens after quadratization. QPBO is used in exactly the example I already gave (computer vision), but there's better ways to solve that computer vision problem (deep neural networks) so QPBO and quadratization are both not needed to to solve that problem.