Abstract Simulating lattice gauge theory (LGT) Hamiltonian and its nontrivial states by programmable quantum devices has attracted numerous attention in recent years. Rydberg atom arrays constitute one of the most rapidly developing arenas for quantum simulation and quantum computing. The Z2 LGT and topological order has been realized in experiments while the U(1) LGT is being worked hard on the way. States of LGT have local constraint and are fragmented into several winding sectors with topological protection. It is therefore difficult to prepare a state in certain sector for experiments, and it is also an important task for quantum topological memory. Here, we propose a protocol of sweeping quantum annealing (SQA) for searching the state within target topological sector. With the Monte Carlo method, we show that this SQA has linear time complexity of size with applications to the antiferromagnetic transverse field Ising model, which has emergent U(1) gauge fields. This SQA protocol can be realized easily on quantum simulation platforms such as Rydberg atoms and superconducting circuits. We expect this approach would provide a generic recipe for resolving the topological hindrances in quantum optimization and the preparation of quantum topological state.
The dynamics of gauge theories is of fundamental interest, with low-dimensional systems displaying a rich phenomenology beyond the rapid thermalization typical of QCD and non-Abelian theories. In particular, recent quantum simulation experiments have reported robust and unexpected signatures of slow relaxation in generic regimes and at large volumes in one-dimensional U(1) lattice gauge theories (LGTs), whose origin remains poorly understood. Here, we present a framework that provides a unified perspective on such slow dynamics and establishes a new route for exploring subdiffusive fractonic hydrodynamics in Rydberg experiments. The backbone of our theory is an exact analytical mapping from U(1) LGTs with a topological
θ angle to non-local kinetically constrained fermionic models with an emergent linear Stark potential. In the absence of the
θ term, this framework interprets the non-thermal dynamics reported in recent experiments as prethermal behavior arising from proximity to an integrable free-fermion model. For non-zero
θ, the emergent Stark potential instead explains the freezing dynamics observed in other recent experiments. We argue that this correspondence could also lead to subdiffusive transport due to emergent conservation laws. We predict that these phenomena arise in a much broader class of models, and support this prediction with numerical simulations and proposals for future experiments.
Lattice gauge theories (LGTs) describe fundamental interactions in particle physics. A central phenomenon in these theories is confinement, which binds quarks and antiquarks into hadrons through the formation of string-like flux tubes of gauge fields. Simulating confinement dynamics is a challenging task, but recent advances in quantum simulation are enabling the exploration of LGTs in regimes beyond the reach of classical computation. For analog devices, a major difficulty is the realization of strong plaquette interactions, which generate string fluctuations that can drive a roughening transition. Understanding string roughening -- where strong transversal functions lead to an effective restoration of translational symmetry at long distances -- is of central importance in the study of confinement. In this work, we show that string roughening emerges naturally in an analog Rydberg quantum simulator. We first map a triangular Rydberg array onto a (2+1)D U(1) LGT where plaquette terms appear as first-order processes. We study flux strings connecting static charges and demonstrate that, near a deconfined quantum critical point, the string exhibits logarithmic growth of its transverse width as the separation between charges increases, along with the universal Lüscher correction to the confining potential -- both signatures of string roughening. Finally, we investigate the real-time dynamics of an initially rigid string, observing large fluctuations after quenching into the roughening regime, as well as string breaking via particle-pair creation. Our results indicate that rough strings can be realized in experimentally accessible quantum simulators, opening the door to detailed studies of how strong fluctuations influence string-breaking dynamics.