  Quantum simulation is one of the major applications of quantum devices. In
the noisy intermediate-scale quantum era, however, the general quantum
simulation is not yet feasible, such as that of lattice gauge theories, which
is likely limited due to the violation of the Gauss law constraint and the
complexity of the real-time dynamics, especially in the deconfined phase.
Inspired by the recent works of S. Ashkenazi and E. Zohar [Phys. Rev. A 105,
022431 (2022)] and of N. Tantivasadakarn, R. Thorngren, A. Vishwanath, and R.
Verresen [arXiv: 2112.01519], we propose to simulate dynamics of lattice gauge
theories by using the Kramers-Wannier transfomation via cluster-state-like
entanglers, mid-circuit measurements and feedforwarded corrections, which
altogether is a constant-depth deterministic operation. In our scheme,
specifically, we first quantum simulate the time evolution under a
corresponding symmetric Hamiltonian from an initial symmetric state, and then
apply the Kramers-Wannier procedure. This results in a wave function that has
time evolved under the corresponding lattice gauge theory from a corresponding
initial, gauged wave function. In the presence of noises in time evolution, the
procedure succeeds when we can pair up magnetic monopoles represented by
non-trivial measurement outcomes. Further, given a noise-free Kramers-Wannier
transformation, the resulting wave function from a noisy time evolution
satisfies the Gauss law constraint. We give explicit examples with the low
dimensional pure gauge theories and gauge theories coupled to bosonic/fermionic
matters such as the Fradkin-Shenker model.
