Resonant false vacuum decay in two dimensions on a 4000-qubit quantum annealer

Problem Statement
Metastable states in many-body physics, such as the false vacuum in quantum field theory and cosmology, typically decay through the nucleation of localized bubbles of the true vacuum, followed by their expansion. Conventional theory treats nucleation and growth as separate stages, with nucleation being the rate-limiting step governed by critical bubble theory. However, the dynamics of post-nucleation growth, particularly in two dimensions, remain less understood. Specifically, it is unclear whether growth itself can become the dominant, nontrivial dynamical regime, controlled by local resonant processes at the bubble boundary rather than by smooth, pressure-driven interface motion. While false vacuum decay (FVD) has been explored in one-dimensional systems and various experimental platforms, the real-time growth of resonant false-vacuum bubbles in two dimensions has largely remained unexplored.

Methodology
The authors investigate this problem using a large-scale programmable quantum annealer (D-Wave Advantage2 systems with over 4000 physical qubits) to realize a two-dimensional mixed-field quantum Ising model on a torus topology. The model is defined by the Hamiltonian:
$$\hat{H} = -J \sum_{\langle i,j \rangle} \hat{\sigma}^z_i \hat{\sigma}^z_j - h_x \sum_i \hat{\sigma}^x_i - h_z \sum_i \hat{\sigma}^z_i$$
where $J \gg h_x$. The system is prepared in a metastable "false vacuum" state (all spins up) with a single "seed" spin flipped to the "true vacuum" state (down) at the center.

The study employs three complementary approaches:

1. Quantum Simulation: Using a reverse-annealing protocol, the authors control the time-dependent transverse field $h_x(t)$ and the longitudinal field $h_z(t)$. They specifically tune $h_z$ to the resonance condition $|h_z| = 2J$. At this value, single-spin flips at the boundary of an existing true-vacuum bubble become energy-conserving (resonant), allowing for kinetically constrained expansion.
2. Tensor-Network Simulations: Tree Tensor Networks (TTNs) are used to simulate the full quantum dynamics of smaller systems ($16 \times 16$ spins) to capture entanglement and verify early-time quantum effects.
3. Stochastic Circuit (SC) Modeling: An effective classical stochastic model is developed to simulate the long-time dynamics of much larger systems (hundreds of thousands of spins). This model enforces the local resonance condition as a constraint on spin flips, allowing for the statistical analysis of bubble growth over extended timescales.

Key Contributions and Results

• Resonant Growth Regime: The authors identify a specific regime where the growth of a true-vacuum domain outpaces spontaneous nucleation by approximately three orders of magnitude. At the resonance $|h_z| = 2J$, the energy cost of creating two additional domain walls is exactly offset by the longitudinal field energy gain from flipping a single spin at the bubble boundary. This makes the growth process a first-order effect in $h_x$, whereas spontaneous nucleation of new bubbles remains a higher-order (fourth-order) process.
• Ballistic Expansion: Experimental data and simulations reveal that the seeded bubble expands with nearly ballistic dynamics. The propagation front follows a light-cone structure with an exponent $p \approx 1$ (where radius $r \sim \tau^p$), indicating that the interface moves at a constant velocity determined by the resonance.
• KPZ Interface Broadening: While the expansion is ballistic, the interface is not rigid. The study observes sub-ballistic broadening of the wavefront. By analyzing the scaling of the interface width, the authors find that the dynamics belong to the Kardar–Parisi–Zhang (KPZ) universality class, characterized by a scaling exponent of $2/3$. This holds true across quantum simulations, TTN calculations, and the stochastic circuit model.
• Quantum Coherence: The authors provide evidence that the observed dynamics are genuinely quantum. The time spent in the resonant regime (tens of nanoseconds) is consistent with coherent operation timescales. Furthermore, the observed scaling of magnetization $M(t) \sim h_x^2 \tau$ arises from the quantum nature of the resonance (resonance width $\delta h_z \propto h_x$), a feature reproduced by TTNs but distinct from classical thermal activation.
• Emergent Isotropy: Despite the underlying $D_4$ symmetry of the square lattice, the averaged bubble growth exhibits remarkable spherical invariance, suggesting that the local resonance rules lead to an emergent isotropic propagation.

Significance
The paper establishes a "growth-dominated" regime of false vacuum decay where the expansion of true-vacuum domains is governed by local resonant processes rather than the standard semiclassical nucleation-and-growth paradigm. The results demonstrate that large-scale quantum simulation can access nonequilibrium metastable dynamics relevant to quantum field theory and cosmology. Specifically, the work shows that programmable quantum hardware can isolate and study specific post-nucleation growth channels, revealing that the asymptotic statistical properties of such growth (ballistic expansion with KPZ broadening) can be captured by effective classical models, even though the underlying microscopic dynamics generate substantial entanglement. This suggests that the large-scale statistical behavior of resonant bubble growth may be robust against microscopic quantum details, while also highlighting the potential for quantum annealers to explore complex many-body dynamics beyond the reach of current classical numerical methods.