Disordered purification phase transition in hybrid random circuits

TL;DR

This paper studies how spatially non-uniform noise affects purification phase transitions in hybrid quantum circuits, revealing changes in critical behavior and entanglement properties due to modulation.

Contribution

It introduces the impact of spatial modulation of measurement probability on purification phase transitions and analyzes the resulting changes in criticality and entanglement.

Findings

Spatial non-uniformity alters the criticality of purification phase transitions.

The correlation length exponent $ u$ shifts from less than 2 to greater than 2 with modulation.

Modulation of two-site gates induces a new phase with short-range entanglement.

Abstract

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 $\nu$ changes from $\nu < 2$ for uniform probability to $\nu > 2$ 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.