Extremely Low-Cost Magic State Preparation toward Fault-Tolerant Quantum Computing
Abstract
Fault-tolerant preparation of non-Clifford resource states is a major contributor to the overhead of quantum computation, motivating protocols that achieve high output fidelity with minimal qubit and circuit costs. We introduce a low-cost magic-state preparation protocol in which the choice of stabilizer generators is co-designed with the flag gadgets, allowing the syndrome-extraction circuit itself to filter correlated faults across a non-Clifford layer. The protocol prepares a logical plus state in the 15-qubit quantum Reed-Muller code, applies a transversal T gate, and gauge-fixes the same register into the seven-qubit Steane code. By reorganizing equivalent Z-type stabilizer generators into jointly flagged measurement groups, the protocol eliminates all accepted logical-error contributions arising from one or two circuit faults under destructive error detection. Under a uniform circuit-level depolarizing noise model, the postselected infidelity is 210.2p3+O(p4). At p=10−3, exact low-order enumeration combined with stratified sampling bounds the infidelity by 2.2×10−7 at 99.9% joint confidence, while retaining an acceptance probability of 86.9%. The complete circuit requires only 19 qubits and 82 CNOT gates. These results demonstrate that stabilizer-generator design can substantially reduce the cost of postselected magic-state preparation, although corrected operation and the fidelity of an unmeasured output block require separate analysis.
Related
- Two-Layer Verification for Fault-Tolerant Magic-State Preparation in High-Rate Quantum Codes
- Fast verification of fault tolerant magic state preparation circuits with the CNOT + T gate set
- Towards fault-tolerant quantum computing with optically controlled superconducting qubits
- Early Fault-Tolerant Magic State Synthesis and Spacetime Efficient Analog Rotations with Color Code on a Superconducting Quantum Processor
- SynDebug: A Framework to Debug Logic Bugs in Fault-Tolerant Quantum Computing Programs
BibTeX
@misc{gao2026extremely,
title = {{Extremely Low-Cost Magic State Preparation toward Fault-Tolerant Quantum Computing}},
author = {Jianshuo Gao and Xiao Yuan and Yuan Yao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12698},
eprint = {2609.12698},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12698},
}
RIS
TY - UNPB
TI - Extremely Low-Cost Magic State Preparation toward Fault-Tolerant Quantum Computing
AU - Jianshuo Gao
AU - Xiao Yuan
AU - Yuan Yao
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.12698
UR - https://arxiv.org/abs/2609.12698
AB - Fault-tolerant preparation of non-Clifford resource states is a major contributor to the overhead of quantum computation, motivating protocols that achieve high output fidelity with minimal qubit and circuit costs. We introduce a low-cost magic-state preparation protocol in which the choice of stabilizer generators is co-designed with the flag gadgets, allowing the syndrome-extraction circuit itself to filter correlated faults across a non-Clifford layer. The protocol prepares a logical plus state in the 15-qubit quantum Reed-Muller code, applies a transversal T gate, and gauge-fixes the same register into the seven-qubit Steane code. By reorganizing equivalent Z-type stabilizer generators into jointly flagged measurement groups, the protocol eliminates all accepted logical-error contributions arising from one or two circuit faults under destructive error detection. Under a uniform circuit-level depolarizing noise model, the postselected infidelity is 210.2p^3+O(p^4). At p=10^−3, exact low-order enumeration combined with stratified sampling bounds the infidelity by 2.2×10^−7 at 99.9% joint confidence, while retaining an acceptance probability of 86.9%. The complete circuit requires only 19 qubits and 82 CNOT gates. These results demonstrate that stabilizer-generator design can substantially reduce the cost of postselected magic-state preparation, although corrected operation and the fidelity of an unmeasured output block require separate analysis.
ER -