Subsystem analysis of continuous-variable resource states

TL;DR

This paper introduces a subsystem decomposition method for analyzing continuous-variable cluster states with GKP encoding, enabling detailed insights into logical information preservation and gate operations in quantum computing.

Contribution

It generalizes the subsystem decomposition approach to CV cluster states with GKP encoding, facilitating analysis of logical information and gate effects in noisy environments.

Findings

Decomposition reveals encoded logical information in CV states.

Quantifies damage to logical qubits during teleportation.

Analyzes the impact of noise on GKP-encoded quantum information.

Abstract

Continuous-variable (CV) cluster states are a universal resource for fault-tolerant quantum computation when supplemented with the Gottesman-Kitaev-Preskill (GKP) bosonic code. We generalize the recently introduced subsystem decomposition of a bosonic code [Phys. Rev. Lett. 125, 040501 (2020)], and we use it to analyze CV cluster-state quantum computing with GKP states. Specifically, we decompose squeezed vacuum states and approximate GKP states to reveal their encoded logical information, and we decompose several gates crucial to CV cluster-state quantum computing. Then, we use the subsystem decomposition to quantify damage to the logical information in approximate GKP states teleported through noisy CV cluster states. Each of these studies uses the subsystem decomposition to circumvent complications arising from the full CV nature of the mode in order to focus on the encoded qubit information.