Umberto Borla

A major goal of the quantum simulation of high-energy physics (HEP) is to probe real-time nonperturbative far-from-equilibrium quantum processes underlying phenomena such as hadronization in quantum chromodynamics (QCD). The quantum simulation of the dynamics of confining strings and glueballs, both essential aspects of quark confinement, in a controllable first-principles way is an important step towards this goal. Here, we realize a $\mathbb{Z}_2$ lattice gauge theory in $2+1$D with a tunable plaquette term on a \texttt{Quantinuum System Model H2} trapped-ion quantum computer. We implement a shallow depth-6 Trotter circuit on a $6 \times 5$ matter-site square lattice utilizing all $56$ available qubits to execute over $1000$ entangling gates. We prepare far-from-equilibrium initial string configurations that we quench across a range of parameters to observe rich dynamical phenomena, such as the formation of gauge-invariant closed-loop excitations reminiscent of glueballs in QCD and multi-order string breaking accompanied by spontaneous matter creation. We further demonstrate experimentally that the system displays genuine $2+1$D dynamics, as evidenced by string snapshots over time that cannot be trivially mapped to $1+1$D physics. Our results demonstrate digital quantum simulations of nonequilibrium dynamics in a higher-dimensional lattice gauge theory and provide an experimentally accessible setting for phenomena related to confinement physics.

The $\mathbb{Z}_2$ lattice gauge theory is a paradigmatic model that exhibits gauge-field-mediated-confinement of pairs of particles into mesons, drawing connections to quantum chromodynamics. In the absence of any additional attractive interactions between particles, mesons are not known to bind in this model. Here, we show that resonant pair-production terms give rise to two separate mechanisms to form stable ``hadron'' bound states of two mesons: either induced by an effective attractive interaction, or a new dynamical binding mechanism induced by an effective repulsion. The repulsively bound hadron is a high-energy state stabilized by being energetically separated from the two-meson continuum through quantum fluctuations of the gauge fields. We study the dynamical formation of this bound state starting from local excitations. We use matrix product state techniques based on the time-evolving block decimation algorithm to perform our numerical simulations and analyze the effect of model parameters on hadron formation. Furthermore, we derive an effective model that explains its formation. Our findings are amenable to experimental observation on modern quantum hardware such as superconducting qubits, trapped ions, and Rydberg atom arrays.

With the advent of advanced quantum processors capable of probing lattice gauge theories (LGTs) in higher spatial dimensions, it is crucial to understand string dynamics in such models to guide upcoming experiments and to make connections to high-energy physics (HEP). Using tensor network methods, we study the far-from-equilibrium quench dynamics of electric flux strings between two static charges in the $2+1$D $\mathbb{Z}_2$ LGT with dynamical matter. We calculate the probabilities of finding the time-evolved wave function in string configurations of the same length as the initial string. At resonances determined by the the electric field strength and the mass, we identify various string breaking processes accompanied with matter creation. Away from resonance strings exhibit intriguing confined dynamics which, for strong electric fields, we fully characterize through effective perturbative models. Starting in maximal-length strings, we find that the wave function enters a dynamical regime where it splits into shorter strings and disconnected loops, with the latter bearing qualitative resemblance to glueballs in quantum chromodynamics (QCD). Our findings can be probed on state-of-the-art superconducting-qubit and trapped-ion quantum processors.