  A previous work demonstrated that quantum simulation of abelian lattice gauge
theories (Wegner models including the toric code in a limit) in general
dimensions can be achieved by local adaptive measurements on symmetry-protected
topological (SPT) states with higher-form generalized global symmetries. The
entanglement structure of the resource SPT state reflects the geometric
structure of the gauge theory. In this work, we explicitly demonstrate the
anomaly inflow mechanism between the deconfining phase of the simulated gauge
theory on the boundary and the SPT state in the bulk, by showing that the
anomalous gauge variation of the boundary state obtained by bulk measurement
matches that of the bulk theory. Moreover, we construct the resource state and
the measurement pattern for the measurement-based quantum simulation of a
lattice gauge theory with a matter field (Fradkin-Shenker model), where a
simple scheme to protect gauge invariance of the simulated state against errors
is proposed. We further consider taking an overlap between the wave function of
the resource state for lattice gauge theories and that of a parameterized
product state, and we derive precise dualities between partition functions with
insertion of defects corresponding to gauging higher-form global symmetries, as
well as measurement-induced phases where states induced by a partial overlap
possess different (symmetry-protected) topological orders. Measurement-assisted
operators to dualize quantum Hamiltonians of lattice gauge theories and their
non-invertibility are also presented.
