  One of the methods proposed in the last years for studying non-perturbative
gauge theory physics is quantum simulation, where lattice gauge theories are
mapped onto quantum devices which can be built in the laboratory, or quantum
computers. While being very promising and already showing some experimental
results, these methods still face several challenges related to the interface
between the technological capabilities and the demands of the simulated models;
in particular, one such challenge is the need to simulate infinitely
dimensional local Hilbert spaces, describing the gauge fields on the links in
the case of compact Lie gauge groups, requiring some truncations and
approximations which are not completely understood or controllable in the
general case. This work proposes a way to obtain arbitrarily large such local
Hilbert spaces by using coarse graining of simple, low dimensional qubit
systems, made of components available on most quantum simulation platforms, and
thus opening the way of new types of lattice gauge theory quantum simulations.
