Nature Communications publishes ion-trap study of thermalization in a 2D lattice gauge theory
In their study "Quantum computing universal thermalization dynamics in a (2+1)D lattice gauge theory", Niklas Mueller, Tianyi Wang, Or Katz, Zohreh Davoudi, and Marko Cetina leveraged a cutting-edge ion-trap quantum computer to experimentally probe the complex process of thermalization in a lattice gauge theory. The findings establish quantum computers as powerful new tools for investigating universal features of thermalization in strongly-correlated quantum matter, and the study has now appeared in Nature Communications.
Thermalization, in simple terms, is how a large isolated quantum system, given enough time, essentially "forgets" its initial state such that, on subsystems, it comes to resemble a maximum entropy state described by thermodynamics. For many quantum systems, this is predicted by the eigenstate thermalization hypothesis (ETH). Recent work and this current study try to elucidate universal feautures of the thermalization dynamics.
Utilizing a trapped-ion quantum computer with all-to-all qubit connectivity, the research team investigated a ℤ$_2$ lattice gauge theory in (2+1) dimensions (two space, one time). Such gauge theories can describe exotic spin-liquid phases of quantum materials, exhibit a confinement-deconfinement phase transition (a simple analog of the color confinement mechanism in quantum chromodynamics—the theory of strong nuclear forces), and topological order in the deconfined phase.
A key innovation was to use randomized-measurement protocols to efficiently extract detailed information about the entanglement structure of the evolving quantum state. Conventional measurements only look at local observables, which often miss the subtle, hidden dynamics of thermalization. By analyzing the entanglement Hamiltonian—an operator whose spectrum describes detailed subsystem entanglement properties—the physicists were able to look for signatures of quantum-chaotic dynamics.
The team focused on two key observables derived from the entanglement Hamiltonian's energy gaps: the gap-ratio distribution and the spectral form factor. These quantities are predicted to signal the onset of quantum chaos, a prerequisite for a system to fully thermalize.
The experimental data successfully showed universal early-time signals for quantum chaos. Specifically, the gap-ratio distribution transitioned from a Poisson distribution, which is characterisitic for unentangled initial states, toward one indicative of quantum chaos and level repulsion, associated with the Gaussian unitary ensemble (GUE) of random matrix theory.
Reference:
N. Mueller, T. Wang, O. Katz, Z. Davoudi and M. Cetina "Quantum computing universal thermalization dynamics in a (2+1)D lattice gauge theory", Nat Commun 16, 5492 (2025), arXiv:2408.00069