Magic State Distillation with the Ternary Golay Code

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.

arXiv comment18 pages, 5 figures. v2: Expanded discussion, accepted in Proceedings of The Royal Society A

References in corpus (35)

• Entanglement of Orbital Angular Momentum States of Photons
• Good Quantum Error-Correcting Codes Exist
• Quantum Teleportation is a Universal Computational Primitive
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Improved Simulation of Stabilizer Circuits
• Multiple Particle Interference and Quantum Error Correction
• Quantum Computing with Very Noisy Devices
• A Theory of Fault-Tolerant Quantum Computation
• Contextuality supplies the magic for quantum computation
• The Resource Theory of Stabilizer Computation
• Restrictions on Transversal Encoded Quantum Gate Sets
• Positive Wigner functions render classical simulation of quantum computation efficient
• Discrete phase space based on finite fields
• Overhead and noise threshold of fault-tolerant quantum error correction
• Negative Quasi-Probability as a Resource for Quantum Computation
• Magic state distillation with low overhead
• Hudson's Theorem for finite-dimensional quantum systems
• SIC-POVMs and the Extended Clifford Group
• Enhanced fault-tolerant quantum computing in $d$-level systems
• Control and Tomography of a Three Level Superconducting Artificial Atom
• Improved magic states distillation for quantum universality
• Classicality in discrete Wigner functions
• Codeword Stabilized Quantum Codes
• Qudit versions of the qubit "pi-over-eight" gate
• Qutrit Magic State Distillation
• Efficiently computable bounds for magic state distillation
• Diagonal gates in the Clifford hierarchy
• Bound States for Magic State Distillation in Fault-Tolerant Quantum Computation
• Qutrit Magic State Distillation Tight in Some Directions
• Noise Thresholds for Higher Dimensional Systems using the Discrete Wigner Function
• Qutrit and Ququint Magic States
• Maximum nonlocality and minimum uncertainty using magic states
• Spectra of phase point operators in odd prime dimensions and the extended Clifford group
• On the classification of Hermitian self-dual additive codes over GF(9)
• Contextual bound states for qudit magic state distillation

Cited by in corpus (10)

• Characterization of Control in a Superconducting Qutrit Using Randomized Benchmarking
• Qutrit and Ququint Magic States
• Knots, links, and long-range magic
• Exact Synthesis of Multiqutrit Clifford-Cyclotomic Circuits
• The Golay codes and Quantum Contextuality
• Scaling W state circuits in the qudit Clifford hierarchy
• Low Overhead Qutrit Magic State Distillation
• Constructing all qutrit controlled Clifford+T gates in Clifford+T
• Transversal AND in Quantum Codes
• Efficient Implementation of a Single-Qutrit Gate Set via Coherent Control