Simulating a measurement-induced phase transition with superconducting qubit arrays

The use of quantum computing is limited until the full development of large-scale fault-tolerant quantum computers. However, state-of-the-art quantum devices can be exploited for quantum simulations to explore exotic and novel physics. Recently, new phase transitions have been described in the entanglement properties of many-body dynamics when unitary evolution is interleaved by measurements, exhibiting universal properties that point to unexplored critical phenomena. Superconducting circuits, in particular arrays of superconducting transmon devices, are among the most promising platforms for quantum simulations. We show numerically that superconducting circuit systems modeled by an attractive Bose Hubbard model interspersed with measurements exhibit a phase transition, from volume-law to area-law, in the entanglement properties of the set of steady-state trajectories, which depends on the probability of measuring. Interestingly, the dispersion in the number of bosons in the half of the array can exhibit a behavior similar to that of entanglement entropy, indicating that it is an experimental candidate to avoid post-selection issues. We also implement the theory of the replica method to describe the model and obtain analytical results that agree with the numerical simulations.