Probing Hadron Scattering in Lattice Gauge Theories on Qudit Quantum Computers

Abstract: An overarching goal in the flourishing field of quantum simulation for high-energy physics is the first-principles study of the microscopic dynamics of scattering processes on a quantum computer. Currently, this is hampered by small system sizes and a restriction to two-level representations of the gauge fields in state-of-the-art quantum simulators. Here, we propose efficient experimentally feasible digital qudit quantum circuits for far-from-equilibrium quench dynamics of a $\mathrm{U}(1)$ quantum link lattice gauge theory, where the electric and gauge fields are represented as spin-$1$ operators. Using dedicated numerical simulations, we probe scattering processes in this model on these proposed circuits, focusing on meson-meson and meson-antimeson collisions. The latter are not possible with a two-level representation of the fields, highlighting the suitability of qudits in exploring scattering processes relevant to quantum electrodynamics. The probed scattering dynamics showcases rich physics, including meson flipping and a reflection-transmission transition in meson-antimeson collisions as a function of the gauge coupling strength. Our simulations, which include realistic noise models of dephasing and depolarization, show very good agreement with the exact noiseless dynamics, signaling the readiness of current qudit platforms to observe microscopic scattering dynamics with significantly shallower circuit depths than their qubit counterparts.