Towards Error-Resilience in Quantum Simulation of Lattice Gauge Theories

Digital quantum simulators may provide a powerful platform for addressing salient questions in a wide variety of fields including particle and condense-matter physics. A particularly rewarding target is given by lattice gauge theories. The fundamental principle of gauge-invariance imposes local gauge constraints upon their constituents, e.g. charged matter and the electric gauge field, which are highly challenging to engineer and which lead to intriguing yet not fully understood features. In this thesis, we simulate the dynamics of a 1+1-dimensional Z2 lattice gauge theory on a superconducting quantum processor. Efficiently synthesising the three-body matter-gauge coupling in the architecture's native gates allows for compact Trotter steps and enables us to reach substantial evolution times. We performed experiments remotely on the processors of Google Quantum AI, as part of their Early Access Program. In these, we observe how tuning a term that couples only to the electric field confines the charges, a manifestation of the tight bond that the local gauge constraints generates between both. At the current scale, the experimental results can still be benchmarked through exact numerics. The use of such quantum technologies to ultimately solve outstanding problems in physics will require to carefully treat errors present in quantum hardware. To this end, we address and mitigate noise via several methods including symmetry verification, Floquet calibration, echo sequences, algorithmic qubit and coupler selection, and assignment averaging. In a parallel effort, we present a procedure to protect quantum simulations of lattice gauge theories against coherent gauge-invariance breaking errors. This technique uses the addition of weighted sums to the system Hamiltonian that are linear in the theory's symmetry generators or local pseudogenerators rendering its resource requirements benign. We make use of this in the experimental implementation to study a further mechanism, where a modification of the gauge constraint from a local Z2 to a local U(1) symmetry freezes the system dynamics. Our work showcases the dramatic restriction that the underlying gauge constraint imposes on the dynamics of a lattice gauge theory, it illustrates how gauge constraints can be modified and protected, and it may promote the study of other models governed by many-body interactions.