Single-shot magic state factories for quantum LDPC codes
Abstract
Quantum low-density parity-check (qLDPC) codes can substantially reduce the qubit overhead of fault-tolerant quantum computation, but any useful architecture based on such codes also requires an efficient mechanism to implement non-Clifford gates in a fault-tolerant manner. We introduce a space-time-efficient magic state factory for high-rate qLDPC codes by combining the transversal non-Clifford gates of recently developed tricycle codes with single-shot four-dimensional balanced product quadcycle codes. The key ingredient is an efficient "escape" mechanism that teleports postselected logical magic states from tricycle codes to larger distance quadcycle codes. Under a standard circuit-level noise model at physical error rate 10−3, our factories produce CCZ states at logical error rates as low as 10−9 with 10-40 times lower space-time cost than state-of-the-art magic state generation methods. The resulting states are directly encoded in high-rate blocks suitable for computation. We identify the quadcycle codes by an AI-assisted search and show that they can serve as excellent memories capable of single-shot error correction. Finally, we present a concrete implementation of the entire factory with highly efficient atom transport on reconfigurable neutral-atom quantum computers. Together, these results provide an end-to-end, practical protocol for producing and utilizing high-fidelity magic states within a high-rate qLDPC architecture, with the lowest space-time cost to date.
Related
- Two-Layer Verification for Fault-Tolerant Magic-State Preparation in High-Rate Quantum Codes
- Magna: simulating magic state factories as cheaply as Clifford circuits
- Symmetry and AI-assisted discovery of magic-state factories
- Sipser-Spielman meets Dijkgraaf-Witten: non-Abelian qLDPC codes via twisted sheaf gauge theory and almost-constant-overhead magic state fountain
- Affine-Profile Stabilizer Thresholds for Magic in Codeword-Stabilized Quantum Codes
BibTeX
@misc{menon2026singleshot,
title = {{Single-shot magic state factories for quantum LDPC codes}},
author = {Varun Menon and Rohan Mehta and Andi Gu and Andrei C. Diaconu and Daniel Bochen Tan and Xiao Xiao and Michael J. Gullans and Qian Xu and Hengyun Zhou and Mikhail D. Lukin and J. Pablo Bonilla Ataides},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10731},
eprint = {2610.10731},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10731},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Single-shot magic state factories for quantum LDPC codes
AU - Varun Menon
AU - Rohan Mehta
AU - Andi Gu
AU - Andrei C. Diaconu
AU - Daniel Bochen Tan
AU - Xiao Xiao
AU - Michael J. Gullans
AU - Qian Xu
AU - Hengyun Zhou
AU - Mikhail D. Lukin
AU - J. Pablo Bonilla Ataides
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10731
UR - https://arxiv.org/abs/2610.10731
AB - Quantum low-density parity-check (qLDPC) codes can substantially reduce the qubit overhead of fault-tolerant quantum computation, but any useful architecture based on such codes also requires an efficient mechanism to implement non-Clifford gates in a fault-tolerant manner. We introduce a space-time-efficient magic state factory for high-rate qLDPC codes by combining the transversal non-Clifford gates of recently developed tricycle codes with single-shot four-dimensional balanced product quadcycle codes. The key ingredient is an efficient "escape" mechanism that teleports postselected logical magic states from tricycle codes to larger distance quadcycle codes. Under a standard circuit-level noise model at physical error rate 10^−3, our factories produce CCZ states at logical error rates as low as 10^−9 with 10-40 times lower space-time cost than state-of-the-art magic state generation methods. The resulting states are directly encoded in high-rate blocks suitable for computation. We identify the quadcycle codes by an AI-assisted search and show that they can serve as excellent memories capable of single-shot error correction. Finally, we present a concrete implementation of the entire factory with highly efficient atom transport on reconfigurable neutral-atom quantum computers. Together, these results provide an end-to-end, practical protocol for producing and utilizing high-fidelity magic states within a high-rate qLDPC architecture, with the lowest space-time cost to date.
ER -