Magic and Entanglement Transitions in Quantum Circuits with Long-Range Interactions

Entanglement is a necessary, but not sufficient, resource to achieve quantum advantage. Magic characterizes the amount of non-Clifford operations needed to prepare quantum states. Gaining insight into the processes that generate or eliminate magic and entanglement is an essential step toward achieving practical fault-tolerant computation. We identify three distinct phase transitions in the magic and entanglement in circuits with non-local unitary dynamics with local projective measurements and a controlled injection of non-Clifford resources. We introduce new algorithms for simulating these circuits and computing the entanglement and magic. These findings offer insight into the relationship between magic and entanglement, which is important for advancing fault-tolerant quantum computation.