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

Using a 4000-qubit quantum annealer to simulate a two-dimensional quantum Ising model, researchers demonstrated a distinct regime of false vacuum decay where local resonance conditions enable kinetically constrained, nearly ballistic domain growth that outpaces nucleation, revealing Kardar-Parisi-Zhang universality in nonequilibrium metastable dynamics.

Original authors: Jaka Vodeb, Gregor Humar, Jean-Yves Desaules, Luka Pavešić, Marko Ljubotina, Zlatko Papic, Kristel Michielsen

Published 2026-08-26

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CC BY 4.0

Original authors: Jaka Vodeb, Gregor Humar, Jean-Yves Desaules, Luka Pavešić, Marko Ljubotina, Zlatko Papic, Kristel Michielsen

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast landscape of the universe, from the birth of stars to the behavior of exotic materials, there exists a peculiar state of being known as a false vacuum. Imagine a ball resting in a shallow dip on a hillside. It is stable enough to stay there for a long time, but it is not at the very bottom of the valley. Given enough time or a strong enough push, the ball will eventually roll out of that dip and tumble down to the true bottom, releasing energy in the process. In the quantum world, this is how a metastable state decays: a system sits in a temporary, higher-energy configuration until a fluctuation triggers a transition to a lower-energy, stable state. This process, called false vacuum decay, is thought to have shaped the early universe and governs the stability of matter itself. Traditionally, scientists believed this transition happened in two distinct steps: first, a tiny bubble of the new, stable state would randomly appear through a rare fluctuation, and second, that bubble would expand to consume the old state. For decades, the focus was almost entirely on the difficult first step—the birth of the bubble—while the subsequent growth was assumed to be a straightforward, pressure-driven expansion.

A team of researchers has now used a massive quantum machine to explore what happens when this second step becomes the dominant and most complex part of the story. Working with a quantum annealer containing more than 4,000 qubits, the scientists created a two-dimensional grid of quantum spins that mimics the behavior of a magnetic material. They prepared the system in a metastable state, essentially a false vacuum, and then introduced a single defect to act as a seed for a new, stable bubble. By carefully tuning the magnetic fields acting on the system, they discovered a specific condition where the growth of this bubble is no longer a slow, steady march. Instead, the expansion becomes incredibly fast, driven by a local resonance that allows the bubble to spread through the material with surprising efficiency.

The experiment revealed a regime where the growth of the true-vacuum domain outpaces the spontaneous creation of new bubbles by a factor of roughly one thousand. This happens because the researchers tuned the system to a point where flipping a single spin at the edge of the bubble costs no energy. In this resonant state, the boundary of the bubble can advance rapidly, spreading outward in a pattern that looks like a branching, fractal tree. The researchers observed this growth in real-time, watching the bubble expand across the quantum processor. The expansion was nearly ballistic, meaning the edge of the bubble moved at a constant, high speed, much like a projectile flying through space. However, the edge was not perfectly sharp or rigid. As the bubble grew, its boundary became slightly fuzzy and irregular, a phenomenon that the team found follows a specific mathematical pattern known as the Kardar-Parisi-Zhang universality class. This pattern describes how interfaces, like the surface of a growing crystal or a spreading liquid, tend to roughen over time in a predictable way.

To confirm that what they saw on the quantum machine was real and not just a glitch of the hardware, the researchers combined their experimental data with advanced computer simulations. They used a technique called tensor networks to model the quantum behavior of smaller systems and a stochastic circuit model to simulate the statistical growth of bubbles in much larger systems. Both methods agreed with the experimental results: the bubble grew ballistically, and its interface broadened in a way that matched the predicted universal scaling laws. The study suggests that the essential physics of this process lies not in the initial formation of the seed, but in the resonant expansion that follows. The researchers found that even though the underlying quantum dynamics generate a significant amount of entanglement, the large-scale statistical behavior of the growing bubble is surprisingly simple and robust.

This work opens a new window into how metastable states decay, showing that under the right conditions, the growth phase can become the primary driver of the process, completely overshadowing the nucleation phase. The findings challenge the standard view that false vacuum decay is always a slow, nucleation-limited event. Instead, they demonstrate that local resonance conditions can trigger a rapid, growth-dominated regime that is accessible and controllable on current quantum hardware. While the experiment was conducted on a specific quantum model, the principles uncovered may have broader implications for understanding phase transitions in quantum materials and even for theories about the early universe. The study establishes that large-scale quantum simulators can now be used to probe these nonequilibrium dynamics with a level of detail that was previously impossible, offering a controlled platform to test ideas that bridge quantum field theory, cosmology, and the physics of strongly correlated matter.

Technical Summary: Resonant False Vacuum Decay in Two Dimensions on a 4000-Qubit Quantum Annealer

Problem Statement
False vacuum decay (FVD) is a fundamental process in quantum field theory and cosmology where a metastable state decays into a lower-energy true vacuum via the nucleation and expansion of bubbles. Conventional theory separates FVD into two distinct phases: the non-trivial nucleation of a critical bubble (driven by fluctuations) and the subsequent, comparatively simple growth driven by free-energy differences. While one-dimensional lattice realizations have revealed resonant nucleation channels, the dynamics of FVD in two dimensions remain poorly understood. Specifically, it is unclear whether a regime exists where post-nucleation growth itself becomes the dominant, non-trivial dynamical process, controlled by local resonant conditions at the bubble interface rather than smooth pressure-driven motion.

Methodology
The authors investigate this problem using a large-scale programmable quantum annealer (D-Wave Advantage2) with over 4,000 physical qubits to simulate a two-dimensional mixed-field quantum Ising model:
$\hat{H} = -J \sum_{\langle i,j \rangle} \hat{\sigma}^z_i \hat{\sigma}^z_j - h_x \sum_i \hat{\sigma}^x_i - h_z \sum_i \hat{\sigma}^z_i$
The system is prepared in a metastable "false vacuum" state (all spins up) with a small transverse field $h_x$ . The researchers utilize a reverse-annealing protocol to control the time-dependent fields.

Key experimental and theoretical components include:

Resonance Tuning: The longitudinal field $h_z$ is tuned to a specific resonance condition, $h_z = 2J$ . At this value, the energy cost of creating a domain wall is exactly offset by the energy gain from flipping a spin at the boundary of an existing true-vacuum bubble. This makes single-spin flips at the interface energy-conserving (resonant).
Seeded Growth: To isolate growth dynamics from spontaneous nucleation, the experiment initializes a single flipped spin (a "seed") at the center of the lattice. The system is then ramped through the $h_z = 2J$ resonance.
Complementary Modeling: The quantum simulation results are validated and extended using two classical approaches:
- Tree Tensor Networks (TTN): Used to simulate the full quantum dynamics on smaller lattices ( $16 \times 16$ ) to capture entanglement and early-time quantum effects.
- Stochastic Circuit (SC) Modeling: A classical effective model where spins flip with a probability constrained by the resonance condition. This allows for the simulation of much larger systems and longer timescales to access asymptotic statistical properties.

Key Contributions and Results
The study identifies and characterizes a distinct "growth-dominated" regime of FVD where the expansion of the true-vacuum domain outpaces spontaneous nucleation by approximately three orders of magnitude.

Resonant Growth Mechanism: At $h_z = 2J$ , the nucleation of a new four-spin bubble is a fourth-order process in $h_x$ , whereas the expansion of an existing bubble via single-spin flips is a first-order process. This hierarchy ensures that once a seed is present, the bubble grows rapidly via resonant interface moves.
Ballistic Expansion: Experimental data and simulations reveal that the seeded bubble expands nearly ballistically. The correlation front propagates linearly with time ( $p \approx 1$ ), forming a clear "light-cone" structure in the magnetization profiles.
KPZ Interface Broadening: While the radial growth is ballistic, the interface of the bubble is not rigid. The wavefront exhibits sub-ballistic broadening. Scaling analysis of the interface width reveals that the fluctuations follow the Kardar–Parisi–Zhang (KPZ) universality class, with a scaling exponent of $2/3$ .
Quantum vs. Classical Dynamics: The TTN simulations show that the process generates significant entanglement, confirming the quantum nature of the dynamics. However, the asymptotic growth laws (ballistic expansion and KPZ broadening) are successfully captured by the classical stochastic circuit model. This suggests that the large-scale statistical properties of the resonant bubble growth are robust and insensitive to many microscopic quantum details.
Scaling Laws: The authors observe a scaling of the magnetization profile $M(t) \sim h_x^2 t$ , which arises from the finite width of the quantum resonance ( $\delta h_z \propto h_x$ ). This scaling is consistent across quantum simulations, TTNs, and the effective resonance model.

Significance and Claims
The paper claims to establish a new route to false vacuum decay where local resonant processes govern the expansion of true-vacuum domains, distinct from the standard semiclassical paradigm of pressure-driven bubble motion.

Platform Capability: The work demonstrates that large-scale quantum annealers can access nonequilibrium metastable dynamics relevant to quantum field theory and cosmology, specifically probing regimes where growth dominates nucleation.
Universality: The results uncover a growth-dominated regime characterized by ballistic expansion and KPZ universality for interface broadening, providing a controlled setting to study these phenomena beyond the standard semiclassical approximation.
Modest Scope: The authors explicitly state that their results isolate a specific post-nucleation growth channel. They do not claim to have solved generic FVD in all contexts but rather identified a specific resonance mechanism that could, in principle, compete with conventional bubble-wall motion. They note that determining how these mechanisms apply to quantum field theory (where expansion is typically pressure-driven) remains an open question requiring further investigation.

In summary, the paper provides experimental and theoretical evidence that in two-dimensional quantum spin systems, resonant conditions can decouple bubble growth from nucleation, leading to a robust, ballistic expansion regime with universal interface fluctuations described by KPZ scaling.

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