Detect anomalous quartic gauge couplings at muon colliders with quantum kernel k-means

In recent years, with the increasing luminosities of colliders, handling the growing amount of data has become a major challenge for future New Physics (NP) phenomenological research. In order to improve efficiency, machine learning algorithms have been introduced into the field of high-energy physics. As a machine learning algorithm, kernel k-means has been demonstrated to be useful for searching NP signals. It is well known that the kernel k-means algorithm can be carried out with the help of quantum computing, which suggests that quantum kernel k-means (QKKM) is also a potential tool for NP phenomenological studies in the future. This paper investigates how to search for NP signals using QKKM. Taking the \(\mu ^+\mu ^-\rightarrow \nu {\bar{\nu }}\gamma \gamma \) process at a muon collider as an example, the dimension-8 operators contributing to anomalous quartic gauge couplings (aQGCs) are studied. The expected coefficient constraints obtained using the QKKM of three different forms of quantum kernels, as well as the constraints obtained by the classical k-means algorithm are presented, and it can be shown that QKKM can help to find the signal of aQGCs. Comparing the classical k-means anomaly detection algorithm with QKKM, it is indicated that the QKKM is able to archive a better cut efficiency.