# Holographic Quantum Circuits from Splitting/Joining Local Quenches

## TL;DR

This paper investigates local quenches in 2D free fermion and holographic CFTs, using entanglement density to understand their properties and proposing new gravity duals resembling quantum circuits.

## Contribution

It introduces entanglement density as a systematic tool for analyzing local quenches and proposes gravity duals akin to quantum circuits based on AdS/BCFT.

## Key findings

- Logarithmic growth of entanglement entropy linked to boundary surface evolution.
- Differences between free and holographic CFTs clarified through entanglement density.
- New gravity duals resembling tensor networks are proposed.

## Abstract

We study three different types of local quenches (local operator, splitting and joining) in both the free fermion and holographic CFTs in two dimensions. We show that the computation of a quantity called entanglement density, provides a systematic method to capture essential properties of local quenches. This allows us to clearly understand the differences between the free and holographic CFTs as well as the distinctions between three local quenches. We also analyze holographic geometries of splitting/joining local quenches using the AdS/BCFT prescription. We show that they are essentially described by time evolutions of boundary surfaces in the bulk AdS. We find that the logarithmic time evolution of entanglement entropy arises from the region behind the Poincare horizon as well as the evolutions of boundary surfaces. In the CFT side, our analysis of entanglement density suggests such a logarithmic growth is due to initial non-local quantum entanglement just after the quench. Finally, by combining our results, we propose a new class of gravity duals, which are analogous to quantum circuits or tensor networks such as MERA, based on the AdS/BCFT construction.