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  • Open Access

Disordered purification phase transition in hybrid random circuits

Kengo Anzai1,2, Hiroaki Matsueda2,3, and Yoshihito Kuno4

  • 1Faculty of Science and Engineering, Akita University, Akita 010-8502, Japan
  • 2Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
  • 3Center for Science and Innovation in Spintronics, Tohoku University, Sendai 980-8577, Japan
  • 4Graduate School of Engineering Science, Akita University, Akita 010-8502, Japan

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Phys. Rev. B 113, 014111 – Published 20 January, 2026

DOI: https://doi.org/10.1103/mb36-pc91

Abstract

Noise is inevitable in realistic quantum circuits. It arises randomly in space. Inspired by the spatial nonuniformity of the noise, we investigate the effects of spatial modulation on quantum phase transitions in a hybrid random Clifford circuit with a mixed initial state. 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 phase transitions and its criticality. We find the effect of spatial nonuniformity in measurement probability on the phase transition. The criticality of the phase transition changes from that of uniform probability, which is elucidated by 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 a 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.

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Phys. Rev. B 113, 014111– Published 20 January, 2026
  • Received 25 July 2025
  • Revised 29 October 2025
  • Accepted 5 December 2025
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