Out-of-equilbrium dynamics of finite qubit systems

We design and simulate symmetry-constrained quantum circuit dynamics that exhibit out-of-equilibrium behavior. Hamiltonian systems with kinetic constraints give rise to Hilbert space fragmentation leading to non-equilibrating dynamics. We generalize the notion of kinetically constrained models with quantum circuits containing only symmetry-respecting gates. We contrast constrained dynamics from quantum circuits containing 4-local gates with those of 2-local gates and a well-studied Hamiltonian with strict kinetic constraints. These are examples of symmetry-constrained quantum circuit dynamics that generate non-equilibrium steady states. The relative entropy and trace distance are utilized as measures to quantify how far these non-equilibrium steady states are from a thermal state.