Abstract:Quantum locally recoverable codes (QLRCs) have recently gained attention as a framework for achieving efficient quantum storage with local recovery capabilities. Analogous to their classical counterparts, QLRCs allow a lost qudit to be reconstructed using only a small subset of other qudits, thereby reducing the resource and operational overhead in recovery. In this work, we extend the study of QLRCs by considering $(r,\delta)$ QLRCs characterized by locality parameter $r$ and local distance $\delta \geq 2$. We present constructions of both random and explicit $(r,\delta)$ QLRCs, including explicit families based on the quantum Tamo--Barg construction. We also present an efficient decoding algorithm for these quantum Tamo--Barg codes.
Furthermore, we introduce quantum \emph{hierarchical} locally recoverable codes (QHLRCs), which extend local recovery to multiple hierarchical levels. For any integer $h\geq 2$, we construct both random and explicit $h$-level QHLRCs, the latter being $h$-level quantum Tamo--Barg codes, and establish a Singleton-like bound for these codes using a CSS framework built from dual-containing classical codes. These results advance the theoretical foundations of quantum erasure recovery and contribute to the design of efficient quantum storage architectures.
From: Pranav Trivedi [view email]
[v1]
Thu, 4 Jun 2026 21:43:20 UTC (90 KB)
[v2]
Wed, 8 Jul 2026 04:19:33 UTC (92 KB)
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