Injection is all you need: parallel universal logic in high-rate concatenated self-dual codes
Abstract
We propose a quantum architecture that achieves addressable and parallel universal fault-tolerant logical in high-rate codes. The codes are obtained from the flexible concatenation of small-distance high-rate self-dual CSS codes. Addressable and parallel universal logic on the resulting K logical qubits is injected by fault-tolerantly preparing and then consuming diverse logical K-qubit CSS stabilizer states and logical lvert H ⟩⊗ K global magic states. Flag-at-origin is used to prepare the stabilizer resource states while a concatenated cultivation protocol prepares the global magic states. These resource states are consumed by Steane-QEC or Knill-QEC teleportation gadgets, which simultaneously perform quantum error correction. Any quantum algorithm with T-depth DT can be executed by consuming 12DT or fewer resource states. We benchmark the fault-tolerant preparation of the resource states for several two-level concatenations of the [[k+4,k,2]] H codes and the Hamming $[[15,7,3]]$ code. In particular, we find that the concatenated cultivation offers at least one order of magnitude spacetime reduction compared to cultivation in the surface code.
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BibTeX
@misc{sullivan2026injection,
title = {{Injection is all you need: parallel universal logic in high-rate concatenated self-dual codes}},
author = {Joseph Sullivan and David Amaro and Michael A. Perlin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30087},
eprint = {2610.30087},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30087},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Injection is all you need: parallel universal logic in high-rate concatenated self-dual codes
AU - Joseph Sullivan
AU - David Amaro
AU - Michael A. Perlin
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30087
UR - https://arxiv.org/abs/2610.30087
AB - We propose a quantum architecture that achieves addressable and parallel universal fault-tolerant logical in high-rate codes. The codes are obtained from the flexible concatenation of small-distance high-rate self-dual CSS codes. Addressable and parallel universal logic on the resulting K logical qubits is injected by fault-tolerantly preparing and then consuming diverse logical K-qubit CSS stabilizer states and logical lvert H ⟩^⊗ K global magic states. Flag-at-origin is used to prepare the stabilizer resource states while a concatenated cultivation protocol prepares the global magic states. These resource states are consumed by Steane-QEC or Knill-QEC teleportation gadgets, which simultaneously perform quantum error correction. Any quantum algorithm with T-depth D_T can be executed by consuming 12D_T or fewer resource states. We benchmark the fault-tolerant preparation of the resource states for several two-level concatenations of the [[k+4,k,2]] H codes and the Hamming $[[15,7,3]]$ code. In particular, we find that the concatenated cultivation offers at least one order of magnitude spacetime reduction compared to cultivation in the surface code.
ER -