Quantum simulation of micro and macro frustrated quantum magnetism with superconducting circuits

We devise a scalable scheme for simulating a Quantum Phase Transition (QPT) from paramagnetic to a frustrated magnetic phase in a network of superconducting flux qubits, and show how it can be characterized both microscop- ically as well as macroscopically, a criterion that is often not satisfied in reporting QPTs. We propose a measure for the macroscopic characterization of our QPT based on the Kullback-Leibler divergence between the obtained and ex- pected probability distributions of the total magnetic moment of the network, whereas microscopic characterization is performed via measuring the local entanglement-witness operator. Our result opens up the possibility for performing QPT experiments that can shed light on the long-standing debate if the macroscopic laws of a system are fundamental, or reducible to the laws of its microscopic constituents.