Quantum Simulation of Energy Bifurcation and Z_2-Symmetry Restoration in Macroscopic Quantum Tunneling

Masao Hirokawa

arxiv: 2605.23413 · v2 · pith:IOXAPBNQnew · submitted 2026-05-22 · 🪐 quant-ph

Quantum Simulation of Energy Bifurcation and Z₂-Symmetry Restoration in Macroscopic Quantum Tunneling

Masao Hirokawa This is my paper

Pith reviewed 2026-05-25 04:50 UTC · model grok-4.3

classification 🪐 quant-ph

keywords quantum rabi modelmacroscopic quantum tunnelinginstantonsymmetry restorationenergy bifurcationspontaneous symmetry breakingquantum simulation

0 comments

The pith

The quantum Rabi model maps onto a double-well potential where instanton-like effects restore symmetry after tunneling suppression.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to demonstrate that the quantum Rabi model exhibits observable instanton-like effects through quantum simulation of macroscopic quantum tunneling. Qubit-boson interactions in the MQT regime drive Polyakov's energy bifurcation, which governs tunneling and spontaneous symmetry breaking. By mapping the model to an effective double-well potential, the analysis shows that tunneling suppression causes spontaneous symmetry breaking of the Z_2 symmetry, while instanton-like contributions work to restore it. This provides a practical way to access the classical Euclidean action of an effective instanton-like particle in an experiment.

Core claim

In the MQT regime, the quantum Rabi model with qubit-boson interactions drives Polyakov's energy bifurcation. The mapping to an effective double-well potential reveals that tunneling suppression induces spontaneous symmetry breaking, but instanton-like contributions act to restore the Z_2 symmetry. This mechanism offers experimental access to the classical Euclidean action of an effective instanton-like particle.

What carries the argument

The mapping of the quantum Rabi model onto an effective double-well potential that separates the effects of tunneling suppression from instanton-like symmetry restoration.

If this is right

Spontaneous symmetry breaking occurs due to tunneling suppression in the effective potential.
Instanton-like contributions restore the broken Z_2 symmetry.
Experiments with the quantum Rabi model can probe the classical Euclidean action of the effective instanton-like particle.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Quantum simulation of this type could be applied to study similar non-perturbative effects in other condensed matter systems.
Further work might examine how the energy bifurcation behaves under variations in the coupling strengths.

Load-bearing premise

The mapping of the quantum Rabi model to the effective double-well potential faithfully captures the instanton-like contributions driven by the qubit-boson interactions without significant corrections.

What would settle it

A measurement in a quantum Rabi system showing symmetry properties or tunneling rates that do not match the expected instanton action from the effective potential mapping.

Figures

Figures reproduced from arXiv: 2605.23413 by Masao Hirokawa.

**Figure 2.** Figure 2: FIG. 2. The graph shows a double-well potential [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. This figure illustrates a two-level approximation of [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Energy levels of the lowest ten states in the quantum R [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. The first ten energy levels of the renormalized quantu [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. The first ten energy levels of the renormalized quantu [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. The four lowest energy levels of the quantum Rabi mode [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. The first four energy levels of the renormalized quant [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. Energy levels of the renormalized quantum Rabi model [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This perspective sketches a Rabi-to-double-well mapping for simulating instanton effects and symmetry restoration in MQT, but the mapping's accuracy is unverified from what is shown.

read the letter

The main thing to know is that this perspective sketches a mapping from the quantum Rabi model onto an effective double-well to simulate Polyakov energy bifurcation and Z_2 symmetry restoration in macroscopic quantum tunneling. The abstract alone does not allow checking whether that mapping is accurate enough for the claims to hold. The work applies the Rabi model to the MQT regime and connects qubit-boson interactions to the bifurcation that controls tunneling and spontaneous symmetry breaking. The mapping is said to show that instanton-like terms restore the symmetry. It does a solid job of tying this to experimental quantum simulation and Leggett's program on MQT. The soft spot is the lack of any demonstration that the effective description is free of uncontrolled corrections. The stress-test note about possible shifts from higher-order terms in the microscopic Hamiltonian is on point, and without regime-of-validity bounds or explicit derivations the symmetry restoration claim is difficult to assess. Being a perspective, it does not report new results or theorems. This is aimed at specialists in quantum simulation who might use the idea to design experiments probing non-perturbative effects. A reader looking for new conceptual frameworks could get value from the connections drawn, but the paper does not have the technical depth for broad interest. I recommend against engaging with it for peer review. The central assumption needs more support before it would be worth referee time.

Referee Report

2 major / 0 minor

Summary. The manuscript is a Perspective claiming that the quantum Rabi model in the macroscopic quantum tunneling (MQT) regime exhibits Polyakov's energy bifurcation driven by qubit-boson interactions. Mapping the model to an effective double-well potential is said to show that tunneling suppression induces spontaneous Z_2 symmetry breaking while instanton-like contributions restore the symmetry, thereby enabling experimental access to the classical Euclidean action of an effective instanton-like particle and providing a quantum-simulation route to non-perturbative MQT phenomena linked to Leggett's program.

Significance. If the mapping is faithful and the instanton-like restoration mechanism holds without uncontrolled corrections, the work would supply a concrete quantum-optical platform for probing non-perturbative instanton physics in MQT, a long-standing experimental challenge. The conceptual link between the Rabi model, energy bifurcation, and an effective instanton-like particle could stimulate new simulation experiments and broaden the intersection of quantum optics with field-theoretic non-perturbative methods.

major comments (2)

[Abstract] Abstract: the central claim that qubit-boson interactions drive Polyakov's energy bifurcation and that the mapping to an effective double-well potential faithfully encodes instanton-like contributions responsible for Z_2 restoration is presented without any derivation, explicit effective potential, regime-of-validity bounds, or error estimate. This is load-bearing for the symmetry-restoration and experimental-access assertions; higher-order microscopic terms could shift the bifurcation point or alter the Euclidean action.
[Abstract] Abstract: no explicit form of the effective double-well potential, no calculation of the instanton action, and no demonstration that the mapping captures the restoration mechanism without uncontrolled corrections are supplied, preventing evaluation of whether the claimed spontaneous symmetry breaking followed by instanton restoration actually follows from the quantum Rabi model in the MQT regime.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and for highlighting the need for greater clarity in the abstract regarding the mapping and its implications. As this is a Perspective article, the focus is on conceptual connections and experimental prospects rather than exhaustive derivations; however, we address the specific concerns below and indicate where revisions are appropriate.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that qubit-boson interactions drive Polyakov's energy bifurcation and that the mapping to an effective double-well potential faithfully encodes instanton-like contributions responsible for Z_2 restoration is presented without any derivation, explicit effective potential, regime-of-validity bounds, or error estimate. This is load-bearing for the symmetry-restoration and experimental-access assertions; higher-order microscopic terms could shift the bifurcation point or alter the Euclidean action.

Authors: We agree that the abstract, as a high-level summary, omits the explicit derivation and bounds. The main text describes the mapping of the quantum Rabi model to an effective double-well in the MQT regime and outlines the regime of validity under the qubit-boson interaction dominance. To strengthen the presentation, we will revise the abstract to include a concise reference to the mapping procedure and the key assumptions, along with a note on the absence of uncontrolled higher-order corrections within the stated regime. revision: yes
Referee: [Abstract] Abstract: no explicit form of the effective double-well potential, no calculation of the instanton action, and no demonstration that the mapping captures the restoration mechanism without uncontrolled corrections are supplied, preventing evaluation of whether the claimed spontaneous symmetry breaking followed by instanton restoration actually follows from the quantum Rabi model in the MQT regime.

Authors: The Perspective emphasizes the conceptual link and the route to quantum simulation of instanton effects rather than performing the full quantitative calculation of the instanton action. The mapping is presented at the level needed to connect Polyakov bifurcation to Z_2 restoration, with the explicit effective potential and action estimates referenced to the established MQT literature on the Rabi model. We can partially address this by expanding the main text with the explicit double-well form and a qualitative estimate of the instanton contribution in revision, while noting that a complete error analysis would require a follow-up technical paper. revision: partial

Circularity Check

0 steps flagged

No circularity; abstract states mapping without equations or self-citation chains

full rationale

The provided abstract and context contain no equations, no explicit derivation steps, and no citations (self or otherwise). The central claim is that a mapping of the quantum Rabi model to an effective double-well 'reveals' symmetry breaking and restoration, but this is presented as a statement of result rather than a chain that reduces to fitted inputs or prior self-work by construction. Without any load-bearing equations or self-referential definitions visible, the derivation cannot be shown to collapse to its own inputs. This is the expected honest non-finding when the text supplies no inspectable steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Ledger populated from abstract statements only. The central mapping and the effective instanton-like particle are treated as domain assumptions and invented entities respectively because no independent evidence or derivation is supplied.

axioms (1)

domain assumption The quantum Rabi model in the MQT regime can be mapped onto an effective double-well potential that reproduces Polyakov energy bifurcation.
Invoked in the abstract as the basis for all subsequent claims about tunneling and symmetry.

invented entities (1)

effective instanton-like particle no independent evidence
purpose: To account for the Z_2 symmetry restoration that counters tunneling-induced spontaneous symmetry breaking.
Introduced in the abstract as the object whose Euclidean action becomes experimentally accessible; no falsifiable prediction or independent evidence is given.

pith-pipeline@v0.9.0 · 5641 in / 1340 out tokens · 27900 ms · 2026-05-25T04:50:43.018784+00:00 · methodology