Grace M. Sommers, Michael Foss-Feig, David Hayes, David A. Huse, Michael J. Gullans (Jun 03 2025).
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
ec≈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.