Quantum Simulation of Macro and Micro Quantum Phase Transition from Paramagnetism to Frustrated Magnetism with a Superconducting Circuit

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 simultaneously. Macroscopic characterization of the quantum phase transition is based on the expected sudden transition of the probability distribution for the spin-network net magnetic moment with this transition quantified by the Kullback-Leibler divergence between measured and theoretical distributions for a given quantum phase. 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 in two ways a quantum phase transition and provide empirical data for revisiting the foundational emergentist-reductionist debate regarding reconciliation of macroscopic thermodynamics with microscopic statistical mechanics especially in the quantum realm for the classically intractable case of frustrated quantum magnetism.