Time-Domain Observables for Resonant Scattering in Quantum Simulations of Lattice Gauge Theory

Abstract

Quantum computing may allow unprecedented access to nonequilibrium quantum dynamics, including problems of interest in particle physics, like the real-time development of scattering processes. Although fault-tolerant simulations at scale are still in the future, recent advancements toward early fault-tolerant simulations motivate building increasingly elaborate benchmark problems in order to assess state-of-the-art capabilities and test new algorithms and observables. In this work, we study glueball scattering on a line-of-plaquettes lattice in pure $SU(3)$ lattice gauge theory. We characterize scattering of the lowest-energy glueball states using classical exact diagonalization methods, identifying the continuum resonance structure using real-time simulations and approximate analytic methods, and we propose time-domain observables for extracting properties of the resonance from quantum simulations. We furthermore construct a toy model that shares the spectral features of the lattice gauge theory and demonstrate extraction of the observables. Feasibility on near-term hardware is demonstrated through simulation of a resonant collision of this toy model on Quantinuum System Model $\texttt{H2-2}$, with a 14-plaquette chain encoded in 28 qubits. The Trotterized circuit after optimization and compression requires $\sim 25n$ entangling gates for $n$ Trotter steps.