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Scientific Reports

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

Masao Hirokawa

Published Oct 27, 2025• 1 citation
Publisher

Abstract

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.

DOI
10.1038/s41598-025-21178-0

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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.
Macroscopic quantum tunneling (MQT), a cornerstone of Leggett's program, is deeply linked with instanton physics, yet its experimental verification remains elusive. This Perspective demonstrates that the quantum Rabi model manifests observable, instanton-like effects via quantum simulation. In the MQT regime, qubit-boson interactions drive Polyakov's energy bifurcation, governing tunneling and spontaneous symmetry breaking. Mapping the quantum Rabi model onto an effective double-well potential reveals that while tunneling suppression induces spontaneous symmetry breaking, instanton-like contributions act to restore it. This mechanism enables experimental access to the classical Euclidean action of an effective instanton-like particle, offering a route to probe non-perturbative phenomena.
We study a quantum-simulation model of a mass enhancement in the fermionic states, as well as in the bosonic ones, of the supersymmetric quantum mechanics. The bosonic and fermionic states are graded by a qubit. This model is so simple that it may be implemented as a quantum simulation of the mass enhancement taking place when supersymmetry (SUSY) is spontaneously broken. Here, our quantum simulation means the realization of the target quantum phenomenon with some quantum-information devices as a physical reality. The model describes how the quasi-particle consisting of the annihilation and creation of 1-mode scalar bosons eats the spin effect given by the X-gate, and how it acquires the mass enhancement in the fermionic states in the spontaneous SUSY breaking. Our model's interaction does not have any Higgs potential. Instead, the qubit acts as a substitute for the Higgs potential by the 2-level-system approximation of the double-well potential, and then, the spontaneous SUSY breaking takes place and the mass is enhanced.
The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal interaction. In the weak coupling regime, it reduces to the well-known Jaynes-Cummings model by applying a rotating wave approximation. The rotating wave approximation breaks down in the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, and remarkable features in the system dynamics are revealed. Here we demonstrate an analog quantum simulation of an effective quantum Rabi model in the ultra-strong coupling regime, achieving a relative coupling ratio of g/ω ~ 0.6. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. We observe fast and periodic quantum state collapses and revivals of the initial qubit state, being the most distinct signature of the synthesized model.An analog quantum simulation scheme has been explored with a quantum hardware based on a superconducting circuit. Here the authors investigate the time evolution of the quantum Rabi model at ultra-strong coupling conditions, which is synthesized by slowing down the system dynamics in an effective frame.
Abstract We study the model of a mass enhancement in the supersymmetric quantum mechanics. This model is so simple that it may be implemented as a quantum simulation of the mass enhancement taking place when supersymmetry (SUSY) is spontaneously broken. It is evolved from a prototype based on the quantum Rabi model. Here, our quantum simulation means the realization of the target quantum phenomenon as a physical entity with some quantum-information devices. The original prototype is given as a mathematical model, and has the transition from the N=2{\mathcal {N}}=2N=2 N = 2 SUSY to its spontaneous breaking, though it has no mass enhancement. It is recently reported that the transition is observed for this prototype in a trapped-ion experiment with devising a method experimentally to realize the transition. The model proposed in this paper describes how the mass enhancement takes place in the fermionic states by the excitation of the 1-mode light boson in the SUSY breaking. In this model, the bosonic and fermionic states are graded by qubits. Although our model’s interaction does not have the Higgs potential, the mass enhancement in the fermionic states is caused by the radiative enhancement with the help of the X-gate’s swap between the fermionic and bosonic states.
The polaron picture is employed to investigate and elucidate the physics of the two-qubit quantum Rabi model, which describes two identical qubits coupled to a common harmonic oscillator. This approach enables us to obtain the ground-state energy and some other simpler physical observables with high accuracy in all regimes of the coupling strengths ggg, while there is no constraint to the ration of tunneling frequency $\mathrm{\ensuremath{\Omega}}$ and field frequency $\ensuremath{\omega}$, which is not simultaneously possible using previous methods. In addition, we also discover a phenomenon that is not present in the one-qubit Rabi model: with the increase of coupling strength ggg, there is a transition of the ground state of the system from a multipolaron state to a bipolaron state. However, the tunneling frequency $\mathrm{\ensuremath{\Omega}}$ counteracts this process. Specifically, when the tunneling frequency $\mathrm{\ensuremath{\Omega}}=0$, the system always stays in the bipolaron state.
We present an alternative way to compute and interpret quantum tunneling in a one-dimensional double-well potential. For large transition time we show that the quantum action functional gives an analytical expression for tunneling amplitudes. This has been confirmed by numerical simulations giving relative errors in the order of ${10}^{\ensuremath{-}5}$. In contrast to the classical potential, the quantum potential has a triple well if the classical wells are deep enough. Its minima are located at the positions of extrema of the ground state wave function. The striking feature is that a single trajectory with a double instanton reproduces the tunneling amplitude. This is in contrast to the standard instanton approach, where infinitely many instantons and anti-instantons have to be taken into account. The quantum action functional is valid in the deep quantum regime in contrast to the semiclassical regime where the standard instanton approach holds. We compare both approaches via numerical simulations. While the standard instanton picture describes only the transition between potential minima of equal depth, the quantum action may give rise to instantons also for asymmetric potential minima. Such a case is illustrated by an example.