Response of quantum spin networks to attacks

TL;DR

This paper studies how quantum spin networks, modeled on various network types, respond to projective measurement attacks, revealing that complex quantum networks are not more robust than simpler ones, contrasting classical network behavior.

Contribution

It introduces a framework to analyze the response of quantum spin networks to attacks using emergent network measures and finds that quantum networks do not exhibit increased robustness due to complexity.

Findings

Emergent networks do not satisfy classical complexity criteria.

Quantum networks respond similarly regardless of network class.

Complex quantum networks are not more robust to attacks than simple ones.

Abstract

We investigate the ground states of spin models defined on networks that we imprint (e.g. non-complex random networks like Erdos-Renyi or complex networks like Watts-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 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 counterintuitive results for our quantum networks. We find that the ground states for Hamiltonians defined on different classes of imprinted networks respond similarly to all our attacks, and the attacks rescale the average properties of the emergent network by a constant factor. Mean field theory explains these results for relatively dense networks, but we also find the simple rescaling behavior away from the regime of validity of mean field theory. 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.