Instanton-like effect caused by qubit-boson interaction in light of quantum simulation

The renormalized quantum Rabi model describing a qubit-boson interaction has the transition from SUSY to its spontaneous breaking under suitable conditions. It is caused by how the X-gate coupled to the Bose field works properly between the two symmetrical wells made by the bosons coupled to a qubit. According to Polyakov's idea, there is the possibility that an instanton tunneling the barrier between those symmetrical wells appears as the classical trajectory. In this paper, therefore, under a physical condition, we show the vestige of the particle like an instanton in the expression of the ground-state energy of the quantum Rabi model.