Response of quantum spin networks to attacks

We numerically investigate ground states of spin models defined on random and complex networks, specifically Erdos-Renyi, Watts-Strogatz, and Barabasi-Albert networks, 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. Counter-intuitive to classical complex networks, we find that the ground states of our spin models respond similarly to attacks, and the resulting properties of the emergent mutual information network are again captured by mean-field theory. Understanding the response of 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.