Observation of a fault tolerance threshold with concatenated codes

Published

December 9, 2025

Author(s)

Grace Sommers, Michael Foss-Feig, David Hayes, David Huse, Michael Gullans

Abstract

We introduce a fault-tolerant protocol for code concatenation using a butterfly network architecture with high noise thresholds and low ancilla overhead to allow implementation on current devices. We develop a probability passing decoder using tensor networks that applies Bayesian updates to the marginal error probabilities after each layer of checks, achieving a state preparation threshold of pc ≈0.089 for erasure errors, and ≈0.015 for unheralded noise. We implement our state preparation protocol on ion-trap hardware with added noise to demonstrate the threshold behavior in a real quantum device. We further theoretically test the performance of our scheme as a quantum memory and for universal quantum computation through the preparation of low-noise magic states for state distillation and T-gate injection.

Citation

Physical Review Research

Volume

7

Issue

4

Pub Type

Journals

Download Paper

https://doi.org/10.1103/v477-jw8l

Local Download

Keywords

quantum computing, quantum error correction, ion traps

Citation

Sommers, G. , Foss-Feig, M. , Hayes, D. , Huse, D. and Gullans, M. (2025), Observation of a fault tolerance threshold with concatenated codes, Physical Review Research, [online], https://doi.org/10.1103/v477-jw8l, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=960165 (Accessed December 16, 2025)