  Quantum simulations of lattice gauge theories for the foreseeable future will
be hampered by limited resources. The historical success of improved lattice
actions in classical simulations strongly suggests that Hamiltonians with
improved discretization errors will reduce quantum resources, i.e. require
$\gtrsim 2^d$ fewer qubits in quantum simulations for lattices with $d$ spatial
dimensions. In this work, we consider $\mathcal{O}(a^2)$-improved Hamiltonians
for pure gauge theories and design the corresponding quantum circuits for its
real-time evolution in terms of primitive gates. An explicit demonstration for
$\mathbb{Z}_2$ gauge theory is presented including exploratory tests using the
ibm_perth device.
