  We design a driven superconducting box with four spins S=1/2 (qubits) such
that coupled devices can give insight on the occurrence of quantum spin liquids
and many-body Majorana states. Within one box or island, we introduce a
generalized nuclear magnetic resonance algorithm to realize our models and
study numerically the spin observables in time as well as the emergent gauge
fields. We discuss the stability of the box towards various detuning effects
and we include dissipation effects through a Lindblad master equation. Coupling
boxes allows us to realize quantum spin liquid phases of Kitaev ${\cal Z}_2$
spin models in various geometries with applications in the toric code. Quantum
phase transitions and Majorana physics might be detected by measuring local
susceptibilities. We show how to produce a N\' eel state of fluxes by coupling
boxes and we address the role of local impurity fluxes leading to random Ising
models. We also present an implementation of the Sachdev-Ye-Kitaev Majorana
model in coupled ladder systems.
