The advantage of simulating lattice field theory with quantum computers is hamstrung by the limited resources that induce large errors from finite volume and sizable lattice spacings. Previous work has shown how classical simulations near the Hamiltonian limit can be used for setting the lattice spacings in real time through analytical continuation, thereby reducing errors in quantum simulations. In this work, we derive perturbative relations between bare and renormalized quantities in Euclidean spacetime at any anisotropy factor - the ratio of spatial to temporal lattice spacings - and in any spatial dimension for U(N) and SU(N). This reduces the required classical preprocessing for quantum simulations. We find less than 10% discrepancy between our perturbative results and those from existing nonperturbative determinations of the anisotropy for SU(2) and U(1) gauge theories. For the discrete groups Z10, Z100 and BI, we perform lattice Monte Carlo simulations to extract anisotropy factors and observe similar agreement with our perturbative results.