Response of quantum spin networks to attacks

We investigate ground states of spin models defined on complex networks that we imprint (e.g., Erdos-Renyi, Wats-Strogatz, and Barabasi-Albert), and their response to decohering processes which we model with network attacks. We quantify the complexity of these ground states, and their response to the attacks, by calculating distributions of network measures of an emergent network whose link weights are the pairwise mutual information between spins. We focus on attacks which projectively measure spins. We find that the emergent networks in the ground state do not satisfy the usual criteria for complexity, and their average properties are captured well by mean field theory and characterized by a single dimensionless parameter in the Hamiltonian. While the response of classical networks to attacks is well-studied, where classical complex networks are known to be more robust to random attacks than random networks, we find counter-intuitive results for our quantum networks. We find that the ground states for Hamiltonians defined on different classes of imprinted networks respond similarly to the attacks, and the resulting properties of the emergent mutual information network are again captured by mean-field theory. We find that the attacks rescale the average properties of the emergent network by a universal function of the dimensionless parameter. Our calculations indicate that complex spin networks are not more robust to projective measurement attacks, and presumably also other quantum attacks, than non-complex spin networks, in contrast to the classical case. Understanding the response of the spin networks to decoherence and attacks will have applications in understanding the physics of open quantum systems, and in designing robust complex quantum systems - possibly even a robust quantum Internet in the long run - that is maximally resistant to decoherence.