# Encoding curved spacetime into initial condition

## TL;DR

This paper demonstrates how to encode curved spacetime geometries into initial quantum states and simulate their effects on a lattice, enabling efficient quantum simulations of curved spacetime physics.

## Contribution

It introduces a method to encode conformal curved spacetime into initial quantum states using unitary rotations, extending previous flat spacetime models.

## Key findings

- The model converges to the Dirac equation in curved spacetime.
- Encoding the metric in initial states simplifies quantum simulation.
- The approach generalizes previous non-unitary rotation methods.

## Abstract

We prove that conformal curved spacetime can be encoded into the initial wave function and that curved propagation can be simulated on a two-dimensional regular lattice with a finite set of homogeneous unitary operators. We generalize recent results shown in [1], where the author transforms flat-spacetime in curved static spacetime via non-unitary rotations. In particular, encoding the metric in the initial quantum state via unitary local rotations, can naturally be useful for quantum simulators due to the efficiency and simplicity of the implementation scheme. We validate our model proving that the continuous limit converges to the Dirac Eq. in curved spacetime.