Long-range measurement-only Clifford circuits display several entanglement and scrambling phases, including a structured-circuit phase with volume-law entanglement, long-range correlations, rapid ancilla purification, and no scrambling.
The projective Heisenberg models also effectively generate the ground state properties of the XX chain with power-law decaying interactions, as we found in Sec
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Entanglement and information scrambling in long-range measurement-only circuits
Long-range measurement-only Clifford circuits display several entanglement and scrambling phases, including a structured-circuit phase with volume-law entanglement, long-range correlations, rapid ancilla purification, and no scrambling.