Nonequilibrium Spin Quantum Networks

Complex systems of relevance to statistical mechanics, strongly correlated systems, information processing and quantum computation can be represented in terms of effective degrees of freedom as classical and quantum many- body spin systems. Spin quantum networks (SQNets) refer to arbitrary many-body spin quantum Hamiltonians with pair- wise interactions in which the coupling between any pair of spins can be represented as an edge in a graph in which each node is occupied by a spin. SQNets naturally account for the family of two-body problem Hamiltonians of relevance to Adiabatic Quantum Computation (AQC). SQNets constitute also a natural platform to explore energy transport in quantum power grids in both natural systems (transport of excitations in chromophores in quantum biology) and artificial systems (engineered quantum matter in platforms for quantum technologies including trapped ions, cold atoms, superconducting qubits, etc.). The description of these networks can be pursued using network theory, whose classical counterpart has revolutionized the understanding of complex systems.