Phase transition and evidence of fast-scrambling phase in measurement-only quantum circuit

Abstract

Information scrambling is nowadays one of the most important topics in various fields of research. Measurement-only circuit (MoC) exhibits specific information scrambling dynamics, depending on the types of projective measurements and their mutual anti-commutativity. The spatial range of the projective measurements in MoCs gives significant influences on circuit dynamics. In this work, we introduce and study long-range MoCs, which exhibit an interesting behavior in their dynamics. In particular, the long-range measurements can induce volume-law phases in MoCs without unitary time evolution, which come from anti-commutative frustration of measurements specific to the long-range MoCs. This phenomenon occurs even in MoCs composed of solely two-body measurements, and it accompanies an entanglement phase transition. Crucially, our numerics find evidences that MoCs can be a fast scrambler. Interplay of high anti-commutativity among measurements and their long-range properties generates fast entanglement growth in the whole system beyond linear-light-cone spreading.

12 pages, 14 figures, accepted in Phys. Rev. B

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• Probing prethermal nonergodicity through measurement outcomes of monitored quantum dynamics
• Measurement-only dynamical phase transition of topological and boundary order in toric code and gauge-Higgs models
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state
• Measurement-only circuit of perturbed toric code on triangular lattice: Topological entanglement, 1-form symmetry and logical qubits
• Disordered purification phase transition in hybrid random circuits
• Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics