Two-Layer Verification for Fault-Tolerant Magic-State Preparation in High-Rate Quantum Codes
Abstract
Encoded magic states are essential for universal fault-tolerant quantum computation, but their resource-efficient preparation in high-rate quantum codes remains challenging. To address this limitation, we propose two-layer verification, which combines local verification of independently prepared subblocks with logical verification after their embedding into a target code. This hierarchy detects harmful error patterns, including even-parity logical-eigenvalue flips that are invisible to a collective product check alone. We demonstrate this scheme for a $[[21,3,5]]$ code by constructing a circuit that embeds three verified seven-qubit Steane-code magic states into the target code. Circuit-level simulations of T- and S-state preparation show logical-error suppression consistent with the code distance. These results demonstrate the potential of two-layer verification as a design principle for reliable magic-state preparation in quantum codes encoding multiple logical qubits.
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BibTeX
@misc{kanomata2026twolayer,
title = {{Two-Layer Verification for Fault-Tolerant Magic-State Preparation in High-Rate Quantum Codes}},
author = {Naoyuki Kanomata and Hayato Goto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32267},
eprint = {2610.32267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32267},
}
RIS
TY - UNPB
TI - Two-Layer Verification for Fault-Tolerant Magic-State Preparation in High-Rate Quantum Codes
AU - Naoyuki Kanomata
AU - Hayato Goto
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32267
UR - https://arxiv.org/abs/2610.32267
AB - Encoded magic states are essential for universal fault-tolerant quantum computation, but their resource-efficient preparation in high-rate quantum codes remains challenging. To address this limitation, we propose two-layer verification, which combines local verification of independently prepared subblocks with logical verification after their embedding into a target code. This hierarchy detects harmful error patterns, including even-parity logical-eigenvalue flips that are invisible to a collective product check alone. We demonstrate this scheme for a $[[21,3,5]]$ code by constructing a circuit that embeds three verified seven-qubit Steane-code magic states into the target code. Circuit-level simulations of T- and S-state preparation show logical-error suppression consistent with the code distance. These results demonstrate the potential of two-layer verification as a design principle for reliable magic-state preparation in quantum codes encoding multiple logical qubits.
ER -