# Complexity and Boost Symmetry

## TL;DR

This paper explores how holographic complexity's time evolution relates to Rindler boost symmetry and firewalls, proposing a novel interpretation involving black and white hole interiors as tapes storing quantum circuit information.

## Contribution

It introduces a new perspective linking complexity dynamics, boost symmetry breaking, and firewalls, with a model of black/white hole interiors as tapes of quantum circuits.

## Key findings

- Boost symmetry controls complexity time dependence.
- Breaking boost symmetry relates to firewall formation.
- Black and white hole interiors act as tapes storing quantum information.

## Abstract

We find that the time dependence of holographic complexity is controlled by the Rindler boost symmetry across the horizon. By studying the collision energy experienced by an infalling object, we see the breaking of this boost symmetry is closely related to firewalls, which in turn shows the connection between the time dependence of complexity and firewalls. We further identify the black and white hole interiors as two tapes storing different parts of the minimal circuit preparing the state. Depending on whether the quantum gates are being laid on the tape at a particular moment, each tape can be in two states: working, or locked. We interpret the existence of firewalls as the locking of tapes.