  One of the difficulties one has to face in the future phenomenological
studies of the new physics~(NP), is the need to deal with increasing amounts of
data. It is therefore increasingly important to improve the efficiency in the
phenomenological study of the NP. Whether it is the use of the Standard Model
effective field theory~(SMEFT), the use of machine learning~(ML) algorithms, or
the use of quantum computing, all are means of improving the efficiency. In
this paper, we use a ML algorithm, the auto-encoder~(AE), to study the
dimension-8 operators in the SMEFT which contribute to the gluon quartic gauge
couplings~(gQGCs) at muon colliders. The AE is one of the ML algorithms that
has the potential to be accelerated by the quantum computing. It is found that
the AE-based anomaly detection algorithm can be used as event selection
strategy to study the gQGCs at the muon colliders, and is effective compared
with traditional event selection strategies.
