Bosonic Pauli+: Efficient Simulation of Concatenated Gottesman-Kitaev-Preskill Codes

A promising route towards fault-tolerant quantum error correction is the concatenation of a Gottesman-Kitaev-Preskill (GKP) code with a qubit code. Development of such concatenated codes requires simulation tools which realistically model noise, while being able to simulate the dynamics of many mode...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Hopfmueller, Florian, Tremblay, Maxime, St-Jean, Philippe, Royer, Baptiste, Marc-Antoine Lemonde
Format: Article
Language:English
Subjects:
Codes
Concatenated codes
Error correction
Fault tolerance
Hilbert space
Qubits (quantum computing)
Simulation
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A promising route towards fault-tolerant quantum error correction is the concatenation of a Gottesman-Kitaev-Preskill (GKP) code with a qubit code. Development of such concatenated codes requires simulation tools which realistically model noise, while being able to simulate the dynamics of many modes. However, so far, large-scale simulation tools for concatenated GKP codes have been limited to idealized noise models and GKP code implementations. Here, we introduce the Bosonic Pauli+ model (BP+), which can be simulated efficiently for a large number of modes, while capturing the rich dynamics in the bosonic multi-mode Hilbert space. We demonstrate the method by simulating a hybrid surface code, where the data qubits are finite-energy GKP qubits stabilized using the small-Big-small (sBs) protocol, and the syndrome qubits are standard two-level systems. Using BP+, we present logical error rates of such an implementation. Confidence in the accuracy of the method is gained by comparing its predictions with full time evolution simulations for several relevant quantum circuits. While developed specifically for GKP qubits stabilized using the sBs protocol, the mathematical structure of BP+ is generic and may be applicable also to the simulation of concatenations using other bosonic codes.
ISSN:2331-8422
DOI:10.48550/arxiv.2402.09333