Averaging symmetric Z_N quantum circuits over random noise produces a noisy surface code whose logical information is protected against symmetric errors up to a threshold, with charge-sharpening transitions coinciding with bulk confinement transitions that differ for N≤4 versus N>4.
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Measurements enhance steady-state entanglement in a paired fermionic chain by suppressing pairing correlations, but the enhancement scales as ln squared L and vanishes in the thermodynamic limit.
Disorder does not alter the presence or absence of measurement-induced phase transitions in noninteracting fermions; the long-time behavior is controlled by the same nonlinear sigma model with renormalized parameters.
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Holographically Emergent Gauge Theory in Symmetric Quantum Circuits
Averaging symmetric Z_N quantum circuits over random noise produces a noisy surface code whose logical information is protected against symmetric errors up to a threshold, with charge-sharpening transitions coinciding with bulk confinement transitions that differ for N≤4 versus N>4.