  This work investigates the application of quantum simulation in the ongoing
"second" quantum revolution, which employs various synthetic quantum matter
platforms, such as ultracold atoms in optical lattices, Rydberg atoms, and
superconducting qubits, to realize exotic condensed matter and particle physics
phenomena with high precision and control. Gauge theories are of particular
interest in modern quantum simulators as they offer a new probe of high-energy
physics on low-energy tabletop devices. However, to accurately model
gauge-theory phenomena on a quantum simulator, stabilizing the underlying gauge
symmetry is crucial. Through this thesis we demonstrate that a recently
developed experimentally feasible scheme based on linear gauge protection,
initially devised to protect against coherent gauge breaking errors, can also
be used to suppress incoherent errors arising from $1/f^{\beta}$ noise
prominent in various quantum simulation platforms. The Bloch-Redfield formalism
is introduced to model gauge violations arising due to these incoherent errors
given the noise power spectrum of the environment. The efficacy of linear gauge
protection in stabilizing salient features of gauge theories in quantum
simulators, such as gauge invariance and exotic far from equilibrium phenomenon
focusing on disorder-free localization, and quantum many-body scars against
$1/f^{\beta}$ noise sources, is illustrated. These results are immediately
applicable in modern analog quantum simulators and digital NISQ devices, paving
the way for further development in the field of quantum simulation of lattice
gauge theories.
