  We devise a scalable scheme for simulating a quantum phase transition from
paramagnetism to frustrated magnetism in a superconducting flux-qubit network,
and we show how to characterize this system experimentally both macroscopically
and microscopically. The proposed macroscopic characterization of the quantum
phase transition is based on the transition of the probability distribution for
the spin-network net magnetic moment with this transition quantified by the
difference between the Kullback-Leibler divergences of the distributions
corresponding to the paramagnetic and frustrated magnetic phases with respect
to the probability distribution at a given time during the transition.
Microscopic characterization of the quantum phase transition is performed using
the standard local-entanglement-witness approach. Simultaneous macro and micro
characterizations of quantum phase transitions would serve to verify a quantum
phase transition in two ways especially in the quantum realm for the
classically intractable case of frustrated quantum magnetism.
