Measurement-Induced Phase Transitions and Logical-Space Localization in Floquet Monitored Clifford Circuits
Abstract
An entanglement transition can occur without a corresponding transition in purification. We demonstrate this separation in spatially local monitored Clifford circuits with a fixed number of layers per Floquet period, where a spatially random pattern of Clifford gates and Pauli measurements is repeated exactly in time. Rare spatial structures persist under this repetition and break the correspondence between entanglement and purification found in conventional spacetime-random circuits. In one spatial dimension, the late-time entanglement produced with an initial product state remains area-law, while the system remains extensively mixed in the thermodynamic and long-time limits if the initial state is maximally mixed. In two or more dimensions, we find a transition between volume-law and area-law entanglement while the system remains mixed on both sides of this transition. An extensive amount of quantum information survives indefinitely in both phases and evolves unitarily despite the repeated measurements. We introduce the logical-support radius to characterize its spatial spreading and identify the volume-law and area-law phases with delocalized and localized logical dynamics, respectively. We further introduce the logical Krylov dimension, which counts the independent logical operators dynamically generated from an initially local operator. Its scaling resolves the transition and provides evidence for a new universality class of measurement-induced phase transitions.
Related
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- Sampling isometric tensor network states with monitored quantum circuits
- Surviving readout errors and incomplete postselection in monitored quantum circuits
- Temporal Interference from Topological Transitions in Monitored Quantum Dynamics
- Entanglement transitions and multifractality in monitored free-fermions with random long-range hopping
BibTeX
@misc{ha2026measurementinduced,
title = {{Measurement-Induced Phase Transitions and Logical-Space Localization in Floquet Monitored Clifford Circuits}},
author = {Hyunsoo Ha and David A. Huse},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25201},
eprint = {2609.25201},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25201},
}
RIS
TY - UNPB
TI - Measurement-Induced Phase Transitions and Logical-Space Localization in Floquet Monitored Clifford Circuits
AU - Hyunsoo Ha
AU - David A. Huse
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.25201
UR - https://arxiv.org/abs/2609.25201
AB - An entanglement transition can occur without a corresponding transition in purification. We demonstrate this separation in spatially local monitored Clifford circuits with a fixed number of layers per Floquet period, where a spatially random pattern of Clifford gates and Pauli measurements is repeated exactly in time. Rare spatial structures persist under this repetition and break the correspondence between entanglement and purification found in conventional spacetime-random circuits. In one spatial dimension, the late-time entanglement produced with an initial product state remains area-law, while the system remains extensively mixed in the thermodynamic and long-time limits if the initial state is maximally mixed. In two or more dimensions, we find a transition between volume-law and area-law entanglement while the system remains mixed on both sides of this transition. An extensive amount of quantum information survives indefinitely in both phases and evolves unitarily despite the repeated measurements. We introduce the logical-support radius to characterize its spatial spreading and identify the volume-law and area-law phases with delocalized and localized logical dynamics, respectively. We further introduce the logical Krylov dimension, which counts the independent logical operators dynamically generated from an initially local operator. Its scaling resolves the transition and provides evidence for a new universality class of measurement-induced phase transitions.
ER -