We identify a new element in quantum simulations of lattice gauge theories, arising from spacetime-dependent quantum corrections in the relation between the link variables defined on the lattice and their continuum counterparts.  While in Euclidean spacetime simulations, based on Monte Carlo sampling, the corresponding tadpole improvement leads to a constant rescaled value per gauge configuration, in Minkowski spacetime simulations it requires a state- and time dependent update of the coefficients of operators involving link variables in the Hamiltonian. To demonstrate this effect, we present the results of numerical simulations of the time evolution of truncated SU(2) plaquette chains and honeycomb lattices in 2+1D, starting from excited states with regions of high energy density, and with and without entanglement.

We would like to thank Randy Lewis for helpful discussions regarding the classical implementation of tadpole improvement. This work was supported, in part, by U.S. Department of Energy, Office of Science, Office of Nuclear Physics, InQubator for Quantum Simulation (IQuS) under Award Number DOE (NP) Award DE-SC0020970 via the program on Quantum Horizons: QIS Research and Innovation for Nuclear Science (Martin, Xiaojun), and by the Quantum Science Center (QSC) which is a National Quantum Information Science Research Center of the U.S. Department of Energy (Marc). This work is also supported, in part, through the Department of Physics and the College of Arts and Sciences at the University of Washington. We have made extensive use of Wolfram Mathematica. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a Department of Energy Office of Science User Facility using NERSC award NP-ERCAP0032083.