  Numerical simulation of lattice gauge theories is an indispensable tool in
high energy physics, and their quantum simulation is expected to become a major
application of quantum computers in the future. In this work, for an Abelian
lattice gauge theory in $d$ spacetime dimensions, we define an entangled
resource state (generalized cluster state) that reflects the spacetime
structure of the gauge theory. We show that sequential single-qubit
measurements with the bases adapted according to the former measurement
outcomes induce a deterministic Hamiltonian quantum simulation of the gauge
theory on the boundary. Our construction includes the $(2+1)$-dimensional
Abelian lattice gauge theory simulated on three-dimensional cluster state as an
example, and generalizes to the simulation of Wegner's lattice models
$M_{(d,n)}$ that involve higher-form Abelian gauge fields. We demonstrate that
the generalized cluster state has a symmetry-protected topological order with
respect to generalized global symmetries that are related to the symmetries of
the simulated gauge theories on the boundary. Our procedure can be generalized
to the simulation of Kitaev's Majorana chain on a fermionic resource state. We
also study the imaginary-time quantum simulation with two-qubit measurements
and post-selections, and a classical-quantum correspondence, where the
statistical partition function of the model $M_{(d,n)}$ is written as the
overlap between the product of two-qubit measurement bases and the wave
function of the generalized cluster state.
