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arXiv · 2506.00579

Observation of a Fault Tolerance Threshold with Concatenated Codes

Grace M. Sommers·Michael Foss-Feig·David Hayes·David A. Huse·Michael J. Gullans
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Abstract

We introduce a fault-tolerant protocol for code concatenation of a generalized Shor code 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 $e_c \approx 0.089$ for erasure errors, and $\approx 0.015$ 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.

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Grace M. Sommers, Michael Foss-Feig, David Hayes, David A. Huse, Michael J. Gullans. 2025-05-31. Observation of a Fault Tolerance Threshold with Concatenated Codes. https://arxiv.org/abs/2506.00579

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