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Two-Dimensional Quantum Simulations of a False Vacuum Decay on a Quantum Annealer

Daniil Teplitskiy

Published Jan 1, 2025• 0 citations
Publisher

Abstract

This work explores the qualitative dynamics of false vacuum decay in two dimensions, focusing on its realization through quantum annealing. Theoretical foundations are outlined and mapped onto quantum hardware, with several encoding strategies evaluated. Among these, the coupled domain wall encoding emerges as the most efficient, minimizing qubit usage while maintaining distance and rotational symmetries crucial for faithful modeling on a QPU. The study also addresses fidelity concerns: instead of the expected uniform distribution in the absence of an encoded potential, the coupled domain wall representation exhibited a bias toward anti-ferromagnetic states, which can be attributed to coupler imperfections. To mitigate this, techniques such as shimming and spin-reversal transformations were tested. Spin-reversal transformations proved to be most effective, both reducing variance as well as eliminating bias without requiring additional corrective iterations, thus offering a lightweight error-mitigation scheme. Building on this foundation, the decay process was simulated using modified Pöschl-Teller potentials combined with a local and global minimum. The results qualitatively reproduced the exponential decay, depending on the distance between the minima, in agreement with semiclassical quantum field theory.

DOI
10.34734/fzj-2026-00477

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This work explores the qualitative dynamics of false vacuum decay in two dimensions, focusing on its realization through quantum annealing. Theoretical foundations are outlined and mapped onto quantum hardware, with several encoding strategies evaluated. Among these, the coupled domain wall encoding emerges as the most efficient, minimizing qubit usage while maintaining distance and rotational symmetries crucial for faithful modeling on a QPU. The study also addresses fidelity concerns: instead of the expected uniform distribution in the absence of an encoded potential, the coupled domain wall representation exhibited a bias toward anti-ferromagnetic states, which can be attributed to coupler imperfections. To mitigate this, techniques such as shimming and spin-reversal transformations were tested. Spin-reversal transformations proved to be most effective, both reducing variance as well as eliminating bias without requiring additional corrective iterations, thus offering a lightweight error-mitigation scheme. Building on this foundation, the decay process was simulated using modified Pöschl-Teller potentials combined with a local and global minimum. The results qualitatively reproduced the exponential decay, depending on the distance between the minima, in agreement with semiclassical quantum field theory.
Abstract From cosmology to quantum matter, metastable states often decay through the nucleation and growth of competing domains, with false vacuum decay providing the paradigmatic example of this process. Here we demonstrate a distinct regime in which domain growth outpaces nucleation by orders of magnitude and is controlled by local resonance conditions. Using a programmable quantum annealer with more than 4000 qubits, we realize a two-dimensional quantum Ising model whose metastable spin-polarized state encodes a false vacuum. At a specific value of the longitudinal field, single-spin flips at the boundary of a seeded bubble become resonant, enabling kinetically constrained expansion. Combining experiment with tensor-network simulations and stochastic circuit modeling, we observe nearly ballistic growth of true-vacuum domains with sub-ballistic interface broadening, consistent with Kardar--Parisi--Zhang universality. Our results establish a growth-dominated regime of false vacuum decay and show how large-scale quantum simulation can access nonequilibrium metastable dynamics relevant to quantum field theory, cosmology, and strongly correlated matter.
From cosmology to quantum matter, metastable states often decay through the nucleation and growth of competing domains, with false vacuum decay providing the paradigmatic example of this process. Here we demonstrate a distinct regime in which domain growth outpaces nucleation by orders of magnitude and is controlled by local resonance conditions. Using a programmable quantum annealer with more than 4000 qubits, we realize a two-dimensional quantum Ising model whose metastable spin-polarized state encodes a false vacuum. At a specific value of the longitudinal field, single-spin flips at the boundary of a seeded bubble become resonant, enabling kinetically constrained expansion. Combining experiment with tensor-network simulations and stochastic circuit modeling, we observe nearly ballistic growth of true-vacuum domains with sub-ballistic interface broadening, consistent with Kardar--Parisi--Zhang universality. Our results establish a growth-dominated regime of false vacuum decay and show how large-scale quantum simulation can access nonequilibrium metastable dynamics relevant to quantum field theory, cosmology, and strongly correlated matter.
Microscopic Dynamics of False Vacuum Decay in the 2+12+12+1D Quantum Ising Model
False vacuum decay, which is understood to happen through bubble nucleation, is a prominent phenomenon relevant to elementary particle physics and early-universe cosmology. Understanding its microscopic dynamics in higher spatial dimensions is currently a major challenge and research thrust. Recent advances in numerical techniques allow for the extraction of related signatures in tractable systems in two spatial dimensions over intermediate timescales. Here, we focus on the 2+12+12+1D quantum Ising model, where a longitudinal field is used to energetically separate the two Z2\mathbb{Z}_2Z2​ symmetry-broken ferromagnetic ground states, turning them into a ``true'' and ``false'' vacuum. Using tree tensor networks, we simulate the microscopic dynamics of a spin-down domain in a spin-up background after a homogeneous quench, with parameters chosen so that the domain corresponds to a bubble of the true vacuum in a false-vacuum background. Our study identifies how the ultimate fate of the bubble -- indefinite expansion or collapse -- depends on its geometrical features and on the microscopic parameters of the Ising Hamiltonian. We further provide a realistic quantum-simulation scheme, aimed at probing bubble dynamics on atomic Rydberg arrays.
We perform an in-depth comparison of quantum annealing with several classical optimization techniques, namely, thermal annealing, Nelder-Mead, and gradient descent. The focus of our study is large quasicontinuous potentials that must be encoded using a domain wall encoding. To do this, it is important to first understand the properties of a system that is discretely encoded onto an annealer, in terms of its quantum phases, and the importance of thermal versus quantum effects. We therefore begin with a direct study of the 2D Ising model on a quantum annealer, and compare its properties directly with those of the thermal 2D Ising model. These properties include an Ising-like phase transition that can be induced by either a change in ``quantumness'' of the theory (by way of the transverse field component on the annealer), or by scaling the Ising couplings up or down. This behavior is in accord with what is expected from the physical understanding of the quantum system. We then go on to demonstrate the efficacy of the quantum annealer at minimizing several increasingly hard two-dimensional potentials. For all potentials, we find the general behavior that Nelder-Mead and gradient descent methods are very susceptible to becoming trapped in false minima, while the thermal anneal method is somewhat better at discovering the true minimum. However, and despite current limitations on its size, the quantum annealer performs a minimization very markedly better than any of these classical techniques. A quantum anneal can be designed so the system almost never gets trapped in a false minimum, and rapidly and successfully minimizes the potentials.
A finite length ferromagnetic chain with opposite spin polarisation imposed at its two ends is one of the simplest frustrated spin models. In the clean classical limit the domain wall inserted on account of the boundary conditions resides with equal probability on any one of the bonds, and the degeneracy is precisely equal to the number of bonds. If quantum mechanics is introduced via a transverse field, the domain wall will behave as a particle in a box, and prefer to be nearer the middle of the chain rather than the ends. A simple characteristic of a real quantum annealer is therefore which of these limits obtains in practice. Here we have used the ferromagnetic chain with antiparallel boundary spins to test a real flux qubit quantum annealer and discover that contrary to both expectations, the domain walls found are non-uniformly distributed on account of effective random longitudinal fields present notwithstanding tuning carried out to zero out such fields when the couplings between qubits are nominally zero. We present a simple derivation of the form of the distribution function for the domain walls, and show also how the effect we have discovered can be used to determine the strength of the effective random fields (noise) characterising the annealer. The noise measured in this fashion is smaller than what is seen during the single-qubit tuning process, but nonetheless qualitatively affects the outcome of the simulation performed by the annealer.
We investigate domain wall confinement and deconfinement through quantum simulation of an effective low-energy Hamiltonian describing the relative motion of a domain wall pair. By mapping the problem onto a discretized Pöschl-Teller potential. Confinement, partial confinement and deconfinement regimes are identified via spatial variance and local probability observables. The close agreement between exact numeric and ideal quantum simulation highlights the emergent single particle description of domain wall physics. Experiments on IBM quantum hardware expose the role of noise and finite-depth dynamics in near-term simulations of non-equilibrium many-body phenomena.