Having Fun with Theoretical Physics

# Celestial Quantum Error Correction

In this project, we initiate the study of Quantum Error Correction in Celestial CFT (CCFT). We start by constructing a toy model with finite degrees of freedom by revisiting noncommutative geometry in Kleinian hyperkähler spacetimes. The model obeys a Wick algebra that renormalizes in the radial direction and admits an isometric embedding à la Gottesman-Kitaev-Preskill. Then we promote qubits to qunits and construct a toy model of CCFT from the perspective of quantum error-correcting codes. In our code, the hard states with quantized BMS soft hair form the logical subspace. This allows us to reverse errors induced by soft radiation. Technically, the construction relies on the recently studied w1+∞ hierarchy of soft currents and its realization in twistor space.

## The Question

The connection between quantum information and holography has been studied extensively, primarily through the AdS/CFT correspondence.

Can we extend analogous concepts to the celestial holography?

## What we can do?

Compared to the holographic code for AdS/CFT, where they started with appreciating the similarities between the AdS/CFT and MERA-like tensor networks, in this series of work we begin by appreciating the same algebraic structure and symmetries that appear in both celestial holography and the Gottesman-Kitaev-Preskill code

## Holographic Code: from qunits to CCFT

In this work, we further exploit the topology of asymptotically flat Kleinian spacetimes to insert certain quantum states, dubbed qunits, at fixed R, as shown in Figure below. The QECC can then be represented as an isometric map where each Hilbert space is a tensor product of N qunits. As it turns out, the number of qunits is proportional to R and hence the dimension of the Hilbert space renormalizes analogously to the AdS case. The setup is presented in the figure below.