A Search for High-Threshold Qutrit Magic State Distillation Routines
<|reference_start|>A Search for High-Threshold Qutrit Magic State Distillation Routines: Determining the best attainable threshold for qudit magic state distillation is directly related to the question of whether or not contextuality is sufficient for universal quantum computation. We carry out a search for high-threshold magic state distillation routines for a highly-symmetric qutrit magic state known as the strange state. Our search covers a large class of $[[n,1]]_3$ qutrit stabilizer codes with up to 23 qutrits, and is facilitated by a theorem that relates the distillation performance of a qudit stabilizer code to its weight-enumerators. We could not find any code with $n<23$ qutrits that distills the strange state with better than linear noise suppression, other than the 11-qutrit Golay code. However, for $n=23$, we find over 600 CSS codes that can distill the qutrit strange state with cubic noise suppression. While none of these codes surpass the threshold of the 11-qutrit Golay code, their existence suggests that, for large codes, the ability to distill the qutrit strange state is somewhat generic.<|reference_end|>
@article{prakash2024a,
    title={A Search for High-Threshold Qutrit Magic State Distillation Routines},
    author={Shiroman Prakash and Rishabh Singhal},
    journal={arXiv preprint arXiv:2408.00436},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.00436},
    primaryClass={quant-ph cs.IT math.CO math.IT}
}