# Modular Bosonic Subsystem Codes

## TL;DR

This paper presents a framework for decomposing bosonic modes into virtual subsystems, enabling the application of qubit-based quantum information techniques to continuous-variable systems, with practical examples involving GKP states and Gaussian cluster states.

## Contribution

It introduces a novel modular decomposition framework for bosonic modes, bridging continuous-variable and qubit-based quantum information processing.

## Key findings

- GKP grid states can be damaged due to entanglement with the gauge mode.
- Qubit cluster states can be identified and disentangled within Gaussian CV cluster states.
- The framework enables new analysis tools for bosonic quantum systems.

## Abstract

We introduce a framework to decompose a bosonic mode into two virtual subsystems-a logical qubit and a gauge mode. This framework allows the entire toolkit of qubit-based quantum information to be applied in the continuous-variable setting. We give a detailed example based on a modular decomposition of the position basis and apply it in two situations. First, we decompose Gottesman-Kitaev-Preskill grid states and find that the encoded logical state can be damaged due to entanglement with the gauge mode. Second, we identify and disentangle qubit cluster states hidden inside of Gaussian continuous-variable cluster states.