Observation of a Fault Tolerance Threshold with Concatenated Codes

• URL: http://arxiv.org/abs/2506.00579v1
• Date: Sat, 31 May 2025 14:24:43 GMT
• Title: Observation of a Fault Tolerance Threshold with Concatenated Codes
• Authors: Grace M. Sommers, Michael Foss-Feig, David Hayes, David A. Huse, Michael J. Gullans,
• Abstract summary: We introduce a fault-tolerant protocol for code concatenation using a butterfly network architecture with high noise thresholds and low ancilla overhead.<n>We develop a probability passing decoder using tensor networks that applies Bayesian updates to the marginal error probabilities after each layer of checks.<n>We implement our state preparation protocol on ion-trap hardware with added noise to demonstrate the threshold behavior in a real quantum device.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $e_c \approx 0.089$ 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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