Floquet evolution of the q-deformed \texorpdfstring{SU(3)${}_1$}{SU(3)1} Yang-Mills theory on a two-leg ladder

Abstract: We simulate Floquet time-evolution of a truncated SU(3) lattice Yang-Mills theory on a two-leg ladder geometry under open boundary conditions using IBM's superconducting 156-qubit device ibm_fez. To this end, we derive the quantum spin representation of the lattice Yang-Mills theory, and compose a quantum circuit carefully tailored to hard wares, reducing the use of CZ gates. Since it is still challenging to simulate Hamiltonian evolution in present noisy quantum processors, we make the step size in the Suzuki-Trotter decomposition very large, and simulate thermalization dynamics in Floquet circuit composed of the Suzuki-Trotter evolution. We demonstrate that IBM's Heron quantum processor can simulate, by error mitigation, Floqeut thermalization dynamics in a large system consisting of $62$ qubits. Our work would be a benchmark for further quantum simulations of lattice gauge theories using real devices.