Dynamical signatures of conventional and asymptotic quantum many-body scars on a trapped ion simulator

One of the promising applications of digital quantum processors is the simulation of many-body quantum systems. They have been already used to investigate several ergodicity violating mechanisms, such as many-body localisation, Hilbert space fragmentation and quantum many-body scars (QMBS). In addition to conventional QMBS, a recently discovered mechanism for ergodicity violation are the so-called asymptotic quantum many-body scars (AQMBS). These become more stable as system size is increased, leading to progressively longer thermalisation timescales. In this work, we show a connection between gapless excitations of certain "reference" Hamiltonians and AQMBS in a related set of Hamiltonian and circuit models. We use this connection to construct a 2-local model hosting both conventional and asymptotic scars. By exploiting the structure of the AQMBS states and the all-to-all connectivity of the Quantinuum H1-1 quantum processor, we prepare these states in logarithmic circuit depth, and probe their thermalisation under Floquet circuit dynamics. Performing simulations with up to 418 entangling ZZ gates, we find slower thermalisation times as the system size is increased, providing experimental signatures of AQMBS.