aiqbench analysis
This paper presents a novel construction of short triorthogonal codes for qudits using a generalized doubling technique, which significantly reduces the resource cost for qutrit magic state distillation in noisy regimes. By combining theoretical insights with exhaustive search results, the authors provide specific code parameters that outperform existing cyclic and Reed-Muller alternatives. These advances directly address efficiency bottlenecks in fault-tolerant quantum computing architectures.
Short qudit triorthogonal codes from doubling
arXiv:2610.29457v1 Announce Type: new Abstract: We construct short triorthogonal codes for qudits of odd prime dimension by generalizing doubling, which combines a triorthogonal code with a code admitting a transversal phase gate, and raises the distance by up to two. This gives codes with parameters $[[28,1,4]]_3$, $[[37,1,5]]_3$, $[[72,1,6]]_3$, $[[118,1,8]]_3$, $[[33,1,5]]_5$ and $[[20,1,4]]_7$, each shorter than the cyclic, concatenated and Reed-Muller codes of the same distance, and a doubling construction of the $[[15,1,3]]_3$ code. When the columns of a generator matrix are regarded as charged points, triorthogonality becomes the vanishing of multipole moments up to octupole order, and doubling becomes a double layer of opposite charges; this picture explains why inputs with nontrivial coefficients can give shorter codes. We also show by exhaustive search that the shortest codes of distance three have length $11$ for $p=5$ and length $7$ for $p=7$. Combined with high-rate distance-two codes, the new codes reduce the cost of qutrit magic state distillation by up to an order of magnitude in regimes with high input noise.
Abstract:We construct short triorthogonal codes for qudits of odd prime dimension by generalizing doubling, which combines a triorthogonal code with a code admitting a transversal phase gate, and raises the distance by up to two. This gives codes with parameters $[[28,1,4]]_3$, $[[37,1,5]]_3$, $[[72,1,6]]_3$, $[[118,1,8]]_3$, $[[33,1,5]]_5$ and $[[20,1,4]]_7$, each shorter than the cyclic, concatenated and Reed-Muller codes of the same distance, and a doubling construction of the $[[15,1,3]]_3$ code. When the columns of a generator matrix are regarded as charged points, triorthogonality becomes the vanishing of multipole moments up to octupole order, and doubling becomes a double layer of opposite charges; this picture explains why inputs with nontrivial coefficients can give shorter codes. We also show by exhaustive search that the shortest codes of distance three have length $11$ for $p=5$ and length $7$ for $p=7$. Combined with high-rate distance-two codes, the new codes reduce the cost of qutrit magic state distillation by up to an order of magnitude in regimes with high input noise.
arXiv:2610.29457 [quant-ph]
(or arXiv:2610.29457v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.29457 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 255 words
