Engineering entanglement geometry via spacetime-modulated measurements

TL;DR

This paper presents a method to engineer specific entanglement geometries in quantum states using spacetime-modulated measurements in monitored quantum circuits, enabling control over holographic entanglement structures.

Contribution

It introduces a novel approach to create arbitrary entanglement geometries via measurement-induced transitions in 1+1D circuits, with concrete protocols for hyperbolic and black hole geometries.

Findings

Successfully engineered hyperbolic and BTZ black hole entanglement geometries.

Numerical verification of entanglement wedge imaging.

Demonstrated feasibility on near-term quantum simulators.

Abstract

We introduce a general approach to realize quantum states with holographic entanglement structure via monitored dynamics. Starting from random unitary circuits in $1+1$ dimensions, we introduce measurements with a spatiotemporally-modulated density. Exploiting the known critical properties of the measurement-induced entanglement transition, this allows us to engineer arbitrary geometries for the bulk space (with a fixed topology). These geometries in turn control the entanglement structure of the boundary (output) state. We demonstrate our approach by giving concrete protocols for two geometries of interest in two dimensions: the hyperbolic half-plane and a spatial section of the BTZ black hole. We numerically verify signatures of the underlying entanglement geometry, including a direct imaging of entanglement wedges by using locally-entangled reference qubits. Our results provide a concrete platform for realizing geometric entanglement structures on near-term quantum simulators.