In this thesis, we analyse indicators of quantum chaos in qubit circuits with simple geometries consisting of many equal two-particle gates, which can be understood as models of 1-dimensional quantum systems. We focus on the level spacing distribution, where symmetries play a central role. In a few chosen geometries, we classify all symmetries, the most interesting of which are space-time symmetries in brickwork and staircase geometries with periodic boundary conditions. They can be explained by expressing the circuit's Floquet operator as a power of some other operator, which we show implies that the Floquet operator belongs to a direct sum of independent circular unitary ensembles. In the context of quantum chaos, this entails behaviour analogous to ordinary unitary symmetries. Qualitatively similar behaviour is also observed under weak symmetry and integrability breaking, where the dependence of the average gap ratio as a function of perturbation strength is analysed.
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