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 $\mathrm{CCZ}$ 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.
Keywords
Subject
Publication details
- Journal
- Not available
- Open access
- Green open access
Cite this article
APA 7
Menon, V., Mehta, R., Gu, A., Diaconu, A. C., Tan, D. B., Xiao, X., Gullans, M. J., Xu, Q., Zhou, H., Lukin, M. D., & Ataides, J. P. B. (2026). Single-shot magic state factories for quantum LDPC codes. https://omanscience.com/en/articles/single-shot-magic-state-factories-for-quantum-ldpc-codes
MLA 9
Menon, Varun, et al. "Single-shot magic state factories for quantum LDPC codes." https://omanscience.com/en/articles/single-shot-magic-state-factories-for-quantum-ldpc-codes.
Chicago (author–date)
Menon, Varun, Rohan Mehta, Andi Gu, Andrei C. Diaconu, Daniel Bochen Tan, Xiao Xiao, Michael J. Gullans, Qian Xu, Hengyun Zhou, Mikhail D. Lukin, and J. Pablo Bonilla Ataides. 2026. "Single-shot magic state factories for quantum LDPC codes." https://omanscience.com/en/articles/single-shot-magic-state-factories-for-quantum-ldpc-codes.
Harvard
Menon, V., Mehta, R., Gu, A., Diaconu, A. C., Tan, D. B., Xiao, X., Gullans, M. J., Xu, Q., Zhou, H., Lukin, M. D. and Ataides, J. P. B. (2026) 'Single-shot magic state factories for quantum LDPC codes', Available at: https://omanscience.com/en/articles/single-shot-magic-state-factories-for-quantum-ldpc-codes.
Vancouver
Menon V, Mehta R, Gu A, Diaconu AC, Tan DB, Xiao X, et al. Single-shot magic state factories for quantum LDPC codes. https://omanscience.com/en/articles/single-shot-magic-state-factories-for-quantum-ldpc-codes
IEEE
V. Menon, R. Mehta, A. Gu, A. C. Diaconu, D. B. Tan, X. Xiao, M. J. Gullans, Q. Xu, H. Zhou, M. D. Lukin, and J. P. B. Ataides, "Single-shot magic state factories for quantum LDPC codes," https://omanscience.com/en/articles/single-shot-magic-state-factories-for-quantum-ldpc-codes.