Phase transition and evidence of fast-scrambling phase in measurement-only quantum circuit

TL;DR

This paper investigates long-range measurement-only quantum circuits, revealing they can induce volume-law phases and exhibit fast entanglement scrambling due to anti-commutative frustration and long-range interactions.

Contribution

It introduces and analyzes long-range measurement-only circuits, demonstrating their ability to produce volume-law phases and fast scrambling behavior without unitary evolution.

Findings

Long-range measurements induce volume-law phases.

Evidence of fast entanglement scrambling in MoCs.

Anti-commutative frustration drives phase transitions.

Abstract

Information scrambling is nowadays one of the most important topics in various fields of research. Measurement-only circuit (MoC) exhibits specific information scrambling dynamics, depending on the types of projective measurements and their mutual anti-commutativity. The spatial range of the projective measurements in MoCs gives significant influences on circuit dynamics. In this work, we introduce and study long-range MoCs, which exhibit an interesting behavior in their dynamics. In particular, the long-range measurements can induce volume-law phases in MoCs without unitary time evolution, which come from anti-commutative frustration of measurements specific to the long-range MoCs. This phenomenon occurs even in MoCs composed of solely two-body measurements, and it accompanies an entanglement phase transition. Crucially, our numerics find evidences that MoCs can be a fast scrambler. Interplay of high anti-commutativity among measurements and their long-range properties generates fast entanglement growth in the whole system beyond linear-light-cone spreading.