Abstract:We generalize the stabilizer formalism for entanglement-assisted quantum error-correcting codes with noisy ebits (EAQECCs-Ne) from the binary case to the general $q$-ary case, where $q$ is a prime power. By leveraging the structure of the generalized Pauli group over $\mathbb{F}_q$ and symplectic geometry over $\mathbb{F}_q^{2n}$, we establish a unified framework for constructing EAQECCs-Ne for qudit systems. Equivalent formulations in terms of symplectic geometry over $\mathbb{F}_q$ and additive codes over $\mathbb{F}_q^{2n}$ are derived. We further construct several families of $q$-ary EAQECCs with noise ebits and analyze their performance compared to optimal stabilizer codes. Our results demonstrate that under certain noise conditions, the proposed EAQECCs-Ne can outperform standard stabilizer codes with equivalent error-correcting capability, offering a promising approach for fault-tolerant quantum computation in high-dimensional quantum systems.
| Subjects: | Quantum Physics (quant-ph); Information Theory (cs.IT) |
| Cite as: | arXiv:2605.23119 [quant-ph] |
| (or arXiv:2605.23119v1 [quant-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2605.23119 arXiv-issued DOI via DataCite (pending registration) |
From: Guanmin Guo [view email]
[v1]
Fri, 22 May 2026 00:42:55 UTC (651 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。