Disordered purification phase transition in hybrid random circuits

Noise is inevitable in realistic quantum circuits. It arises randomly in space. Inspired by spatial non-uniformity of the noise, we investigate the effects of spatial modulation on purification phase transitions in a hybrid random Clifford circuit. As an efficient observable for extracting quantum entanglement in mixed states, we employ many-body negativity. The behavior of the many-body negativity well characterizes the presence of the purification phase transitions and its criticality. We find the effect of spatial non-uniformity in measurement probability on purification phase transition. The criticality of the purification phase transition changes from that of uniform probability, which is elucidated from the argument of the Harris criterion. The critical correlation length exponent $ν$ changes from $ν< 2$ for uniform probability to $ν> 2$ for spatially modulated probability. We further investigate a setting where two-site random Clifford gate becomes spatially (quasi-)modulated. We find that the modulation induces a phase transition, leading to a different pure phase where a short-range quantum entanglement remains.

💡 Research Summary

This paper investigates how spatially non‑uniform noise—implemented as site‑dependent measurement probabilities or modulated two‑qubit Clifford gates—affects purification phase transitions in one‑dimensional hybrid random Clifford circuits. The authors use two diagnostics: logarithmic purity (the second‑Renyi entropy of the density matrix) and many‑body negativity (MBN), an entanglement measure that remains meaningful for mixed states.

First, they reproduce the known purification transition for uniform measurement probability p, finding a critical point p_c≈0.159 and a correlation‑length exponent ν≈1.2 from purity scaling, while MBN yields ν≈1.56. Both observables show a volume‑law (mixed) phase for p<p_c and an area‑law (pure) phase for p>p_c.

Next, they introduce spatial modulation of the measurement probability: each site i has p_i = w_i n⁻¹ with w_i uniformly random in