Magic State Distillation with the Ternary Golay Code

2020/03/31 by Shiroman Prakash · 1 citation
Computer Science · Materials Science · Physics and Astronomy · #Binary Golay code #Chemical and Physical Properties of Materials #Error detection and correction #MAGIC (telescope) #Quadratic equation #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Qubit #Qutrit #Ternary Golay code #Ternary operation #msc:81P70 #quant-ph

paper · pdf · doi:10.1098/rspa.2020.0187

published as Proc. R. Soc. A. 476: 20200187 (September, 2020) · 18 pages, 5 figures. v2: Expanded discussion, accepted in Proceedings of The Royal Society A

openalex publication_date 2020/09/01 · arxiv created 2020/09/04 · arxiv updated 2020/09/07 · openalex created_date 2020/09/08 · openalex updated_date 2026/08/05

Abstract

The ternary Golay code -- one of the first and most beautiful classical error-correcting codes discovered -- naturally gives rise to an 11-qutrit quantum error correcting code. We apply this code to magic state distillation, a leading approach to fault-tolerant quantum computing. We find that the 11-qutrit Golay code can distill the "most magic" qutrit state -- an eigenstate of the qutrit Fourier transform known as the strange state -- with cubic error-suppression and a remarkably high threshold. It also distills the "second-most magic" qutrit state, the Norell state, with quadratic error-suppression and an equally high threshold to depolarizing noise.

Citations

• Qudit versions of the qubitπ/8gate
• Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations
• Maximum nonlocality and minimum uncertainty using magic states
• Classicality in discrete Wigner functions
• Improved simulation of stabilizer circuits
• Control and Tomography of a Three Level Superconducting Artificial Atom
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Good Quantum Error-Correcting Codes Exist
• At the Dawn of the Theory of Codes
• Diagonal gates in the Clifford hierarchy
• On the Quantum Correction For Thermodynamic Equilibrium

Cited by

• Ternary Golay code [wikipedia]

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