We propose a novel platform for the study of quantum phase transitions in one dimension (1D QPT). The system consists of a specially designed chain of asymmetric SQUIDs; each SQUID contains several Josephson junctions with one junction shared between the nearest-neighbor SQUIDs.We develop the theoretical description of the low energy part of the spectrum. In particular, we show that the system exhibits the quantum phase transition of Ising type. In the vicinity of the transition the low energy excitations of the system can be described by Majorana fermions. This allow us to compute the matrix elements of the physical perturbations in the low energy sector. In the microwave experiments with this system, we explored the phase boundaries between the ordered and disordered phases and the critical behavior of the systems low-energy modes close to the transition. Due to the flexible chain design and control of the parameters of individual Josephson junctions, future experiments will be able to address the effects of non-integrability and disorder on the 1D QPT.
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