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Continuous gauge theories, because of their bosonic degrees of freedom, have
an infinite-dimensional local Hilbert space. Encoding these degrees of freedom
on qubit-based hardware demands some sort of ``qubitization'' scheme, where one
approximates the behavior of a theory while using only finitely many degrees of
freedom. We propose a novel qubitization strategy for gauge theories, called
``fuzzy gauge theory,'' building on the success of the fuzzy $\sigma$-model in
earlier work. We provide arguments that the fuzzy gauge theory lies in the same
universality class as regular gauge theory, in which case its use would obviate
the need of any further limit besides the usual spatial continuum limit.
Furthermore, we demonstrate that these models are relatively resource-efficient
for quantum simulations.
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