  The Hamiltonian limit of lattice gauge theories can be found by extrapolating
the results of anisotropic lattice computations, i.e., computations using
lattice actions with different temporal and spatial lattice spacings ($a_t\neq
a_s$), to the limit of $a_t\to 0$. In this work, we present a study of this
Hamiltonian limit for a Euclidean $U(1)$ gauge theory in 2+1 dimensions (QED3),
regularized on a toroidal lattice. The limit is found using the renormalized
anisotropy $\xi_R=a_t/a_s$, by sending $\xi_R \to 0$ while keeping the spatial
lattice spacing constant. We compute $\xi_R$ in $3$ different ways: using both
the ``normal'' and the ``sideways'' static quark potential, as well as the
gradient flow evolution of gauge fields. The latter approach will be
particularly relevant for future investigations of combining quantum
computations with classical Monte Carlo computations, which requires the
matching of lattice results obtained in the Hamiltonian and Lagrangian
formalisms.
